text:
# WCPE III 2021 Hanoi, VIETNAM

Dec 13 – 16, 2021
Europe/Zurich timezone
All revisions have been received. We hope to bring you the results soon (in March that is).

## Astronomical Methods and the Terrestrial Climate: An Estimation of the Earth's Albedo Based on Self-obtained Data

Dec 14, 2021, 11:20 AM
20m
Zoom ID: 701 110 5119, Passcode: 12345 (Zoom 3)

### Zoom ID: 701 110 5119, Passcode: 12345

#### Zoom 3

Keep Zoom ID, Passcode confidential. This is only for WPCE-3 participants.
Presentations in Wroclaw 20. Contemporary physics and modern physics in schools and universities

### Speaker

Simon Kraus (University of Siegen)

### Description

The significance of the albedo for the terrestrial climate
The albedo is defined as the ratio of reflected to incident light on a body in the case of diffuse reflection. For celestial bodies—such as the planets, asteroids or comets—the albedo is an essential quantity, because on the one hand it determines their visibility and on the other hand it allows statements about their surface properties. Already the comparison of different planets and moons yields astonishing results: The albedo of the earth is about three times higher than that of the moon, which appears very bright and white. In general, the albedo of planets with an atmosphere is significantly higher than that of planets or moons an atmosphere and with a rocky surface. An exception is again the very fresh ice surface of Saturn's moon Enceladus. Here there is a clear difference to the likewise icy, but very dark cometary surfaces, whose albedo is comparable to fresh asphalt. [1]
For the Earth’s climate the albedo of the planet is of very high importance. In educational contexts, the mean surface temperature of the Earth is often calculated based on the balance of incident solar energy $E_in=G_SC\ \pi R_E^2$ to the emitted energy $E_{out}=4\pi R_E^2\ \sigma_{SB}\ T^4$ across the Earth's surface. [2, 3] Here $G_{SC}$ is the solar constant, $R_E$ is the Earth's radius, and $\sigma_{SB}$ is the Stefan-Boltzmann constant. However, in order to obtain an approximately correct result, the irradiated energy must be reduced by a certain factor, which results just from the Earth’s albedo $A$. It causes a considerable part of the solar radiation to be reflected before it becomes effective in the climate system. This modification for the albedo results in the effective irradiated energy: $E_{eff}=G_{SC}\ \pi\ R_E^2\ \ (1-A)$.
The numerical value for the albedo is usually given at this point and used as a global mean value of $A=0.3$. However, due to its importance, it seems desirable to also teach the method behind the determination of this value and to enable students at an undergraduate level to collect and evaluate their own data on the Earth's albedo.

Estimation of the albedo on the basis of self-performed measurements
The method for the determination of the Earth’s albedo requires for its practical realization, besides some basic astronomical data, hardly more than the knowledge of the phase function of the moon (which is assumed to be known here) and intensity measurements for the illuminated ($I_{bright}$) and the non-illuminated side ($I_{dark}$) of the moon. The brightness of the unlit part of the lunar surface is never zero, because at any time light from the Earth (both from the atmosphere and from the surface) is scattered towards the Moon. From geometrical considerations the albedo of the earth can then be concluded from the ratio of the intensities [3]: $A\propto\ \ I_ {dark}/I_{bright}$.

This contribution will focus on the handling of the obtained data, the factors influencing their quality, possible improvements in data collection as well as the general limitations and further potentials of the method. For example, the influence of scattered light is a major challenge, which can, however, be countered by means of suitable procedures if the observation conditions are good. However, this requires that there is no excessive contribution from external light sources, especially if these cause reflections within the telescope optics. The exact procedures for data acquisition, i.e., the selected patches on the lunar surface, also represent a potential source of measurement uncertainties, where a balance must be found between the effort required to analyze the data and the desired accuracy.

Conclusion
The Earth's albedo, as an essential factor for modeling the terrestrial climate, can be derived with sufficient accuracy for educational purposes from data which is obtained with simple instruments. For the evaluation, the handling of external influences on the measured intensities and the conditions of the measurement play a role above all. A discussion of the individual factors, as well as strategies for dealing with them, can provide valuable insights into the acquisition and processing of observational data.

References

Lamy, P. L., Toth, I., Fernandez, Y. R., & Weaver, H. A. (2004). The sizes, shapes, albedos, and colors of cometary nuclei. In M. C. Festou, H. U. Keller, & H. A. Weaver (Eds.), Comets II (p. 223).
Shallcross, D. E., & Harrison, T. G. (2007). Climate change made simple. Physics Education, 42(6), 592–597.
Forinash, K. (2016). A few ideas for teaching environmental physics. Physics Education, 51(6), 65024.
Kraus, Simon F. (2021): Measuring the Earth's albedo with simple instruments. In: Eur. J. Phys. 42 (3). DOI: 10.1088/1361-6404/abe8e4.

### Primary author

Simon Kraus (University of Siegen)


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# Implicit Differentiation

1. Jul 26, 2007

### homology

Hi guys,

I have a question on an implicit differentiation problem. I get two different answers depending on how I do it and the answers are different (not just looking, but different).

The problem is $$\frac{x+3}{y}-4x-y^2=0 [\tex]. One option is to just differentiate as it stands and you get [tex] y'=\frac{y-4y^2}{x+3+2y^3} [\tex]. Another possibility is to initially multiply both sides of the equation by y to simplify it. If you do that the derivative you obtain is [tex] y'=\frac{1-4x}{4x-3y^2} [\tex]. These are two different derivatives but I'm not sure why this happens. Any thoughts would be appreciated (NOTE: I'm teaching the course and this came up). P.S. why aren't my equations tex-ing? Kevin 2. Jul 26, 2007 ### cliowa Your eqns aren't texing because the end command is [ / tex] instead of your backslash. The point is that you define a function y implicitly. What makes you think you're allowed to multiply by y and obtain the same result? The statement you get surely is true (multiplying 0 by anything will yield 0, true), but it might simply define a different function y. See? You could multiply by anything, say xy, but the expression you get will not be equivalent to the thing you started with. When you multiply by 0 there's a loss of information. 3. Jul 26, 2007 ### rocomath since they're not working, can you just type it out normally. i'm getting so confused as to what the problem is, lol. 4. Jul 26, 2007 ### homology Here is the original problem: The problem is [tex] \frac{x+3}{y}-4x-y^2=0$$. One option is to just differentiate as it stands and you get $$y'=\frac{y-4y^2}{x+3+2y^3}$$. Another possibility is to initially multiply both sides of the equation by y to simplify it. If you do that the derivative you obtain is $$y'=\frac{1-4y}{4x+3y^2}$$. These are two different derivatives but I'm not sure why this happens.

This is something subtle I think. If you take the original equation and multiply by y you get $$x+3-4xy-y^3=0$$. You can solve for $$x+3$$ to get $$x+3 = 4xy+y^3$$. Then plug this into the derivative obtained by straight implicit differentiation (i.e. $$y'=\frac{y-4y^2}{x+3+2y^3}$$) and with a bit of algebra you get the other function.

Now, I plotted both of these "derivatives" as functions of (x,y) and they are different functions. However, when we restrict their domain to that subset of the plane which represents the graph of the original function, they agree. That strikes me as interesting. How many functions could you have that all agreed on that same point set that you could arrive at through implicit differentiation? Probably a lot.

Any thoughts or comments would be well appreciated,

Kevin

Last edited: Jul 27, 2007
5. Jul 26, 2007

### cliowa

6. Jul 26, 2007

### rocomath

could you show your steps for y' = 1-4x / 4x-3y^2

this so far is your best solution but it's still not right. kind of close tho.

7. Jul 26, 2007

### truewt

why is that so? As long as y is a function of x, and y is non-zero, why is multiplying the equation by y leading to a different deriavative of y?

8. Jul 26, 2007

### homology

Oops, that was a typo, I'll edit the post

9. Jul 26, 2007

### homology

cliowa,

I didn't respond, because it doesn't matter. y=0 isn't in the domain, multiplying by y is find otherwise.

Thanks though,

Kevin

10. Jul 27, 2007

### RohanSingh

Both the expressions for y' are correct. easy manipulation of y^3 will get u the equality.

the second expression for y' is wrong

11. Jul 27, 2007

### homology

RohanSingh: did you mean the minus sign in the bottom, sorry another typo. Nevertheless, noone seems particularly interested in the nature of the problem. The two derivatives are not, in general equal, they are only equal on limited portions of their domains, in particular the point set that represents the graph of the implicit function. That's interesting to me.

So, for the record, I know both derivatives are correct (typos aside).

Thanks,

Kevin

12. Jul 27, 2007

### cliowa

If you multiply by y, your answer will be the same as long as you stick with your initial domain, which excludes y=0. So surely the two results must agree on the level sets of your first equation. But, that's what I was trying to say, if you multiply by anything you might get a new level set, which contains the old one, and new values for the derivative. Try multiplying by xy for example, and you get a new answer. That however isn't surprising, because the domain of y' as you calculate it implicitly really only are those x where y(x) is part of the level set implicitly defined. The algebraic expression you get may be extendable, but that concerns a new, different function then.

Well, the two derivatives are not defined in general! My differentiating implicitly you assume that your always on the level set. As I mentioned above, there's no validity to the derivatives outside the domain of the original function. Do you know what I mean?

Last edited: Jul 27, 2007
13. Jul 27, 2007

It is easy to see that both are equal by dividing the top and bottom of the first expression by y, and then using the definition of y.

14. Jul 27, 2007

### cliowa

Thanks, DeadWolfe, that's exactly what I'm saying: You need to use the definition of y, the level set.

15. Jul 27, 2007

### homology

Thanks for the discussion guys. Nevertheless, it never occured to me that this happens. It doesn't happen for functions, just implicit functions. As derivatives they're not defined on anything but the limit set, but they are functions in their own right, and I still think its interesting. I just think there might be some interesting math in here. Differentaition of implicitly defined curves maps maps these curves into subsets of a function space. I haven't thought about it much, but it might be fun to see if the functions that agree on the level sets could form some sort of equivalence class and so you could look at some sort of quotient structure and see what comes out of it.

I'm excited because this makes implicit functions interesting to me, I haven't ever seen much use in them so its nice to ponder something.

Kevin

16. Jul 27, 2007

### rocomath

you can definitely apply this technique for optimization.

in Stewart's Calculus, he did an example that took so many damn steps, then he showed it through implicit differentiation and it was like 1/4 the agony of doing it the long way ... i was like wow.

Last edited: Jul 27, 2007
17. Jul 29, 2007

### homology

I don't have a copy of stewart's, could you outline the problem statement?

Thanks,

Kevin

18. Jul 29, 2007

### rocomath

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can.

You need the Volume & SA Formula.

19. Aug 3, 2007

### homology

Thanks for the example, however I don't see why you'd need implicit differentiation. Set V=1 and solve for h in the formula for a volume of a cylinder and jam that into the formula for Surface area of a cylinder and differentiate it. It is minimized by a radius of (1/(2pi))^(1/3) and a height of (1/pi)(2pi)^(2/3). Seems pretty standard. I'm still looking for an example that would justify implicit differentiation.

Thanks,

Kevin

format: plain


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# Information Retrieval Lab: Basic Retrieval¶

In this exercise, we will implement a basic retrieval model. While we already answered some questions using term statistics in the indexing exercise, this lab introduces the concept of a relevance function: a way of quantifying the relevance between a query (expressing a users information need) and a document (potentially fulfilling an information need).

## Lecture Recall¶

First, recall some important concepts from the lecture: indexing, term weighting, document representations, query and query representations.

###### Indexing¶

Gather and store auxiliary information about documents, required for fast online query processing (i.e., to score and rank documents when a query is submitted). Such information may include term frequencies, document frequencies, document lengths, ... The data structure used is a key-value store (i.e., a hash map).

###### Term Weighting¶

For each index term of a document, calculate a weight indicating its importance with respect to the document, allowing for document scoring with respect to a query. Common term weighting schemes are term-frequency (tf), term-frequency-inverse-document-frequency (tfidf), BM25, ...

###### Document representations¶

The representation of a document $d$ is a $|T|$-dimensional vector, where the $i$-th vector component of $d$ corresponds to a term weight $w_i$ of term $t_i \in T$, indicating its importance for $d$.

###### Query¶

A inquiry string expressing a users information need, either in natural or in a specialized query language.

###### Query representations¶

A query representation $q$ is constructed like a document representation, but for a user-supplied query instead of a document.

## Setup¶

To implement a scoring model, we first import existing code from the previous exercises. We will make use of the Shakespeare document collection, the preprocessing component and the index. We supply a reference solution you can import, but feel free to continue using your own code!

Exercise: using the code from previous exercises, construct an index on top of the Shakespeare document collection.

In [ ]:
from modules.shakespeare import corpus
from modules.preprocessing import PreprocessorSpacy as Preprocessor
from modules.indexing import Index

# Your code here

## Term Weighting¶

To compute document representations, we first need to implement term weighting. For the purposes of this exercise, we choose the term-frequency-inverse-document-frequency (TFIDF) weighting scheme, given by the following equation: $tfidf = tf \cdot idf$, where $tf(t,d)$ is the normalized term frequency, denoting the importance of a term $t$ in document $d$, and $idf(t, D) = \log\frac{|D|}{df(t,d)}$ is the inverse document frequency, denoting the importance of term $t$ in general.

Note that different approaches to normalizing the term frequency exist. For this exercise, we use the following normalization:

$$1 + \log(\text{tf}(t,d))\text{ for tf}(t,d)> 0$$

Exercise: implement the tfidf term weighting function.

In [ ]:
from math import log

def tfidf(term_frequency: int, document_frequency: int, document_count: int) -> float:
"""
Term-frequency-inverted-document-frequency, which calculates the tfidf for a given term frequency, document frequency and document count.
:param term_frequency: The frequency of the term in the document.
:param document_frequency:
:param document_count:
:returns: tfidf score
"""
# Your code here

## Document Representation¶

The representation $d$ of a document $D$ is a $|T|$-dimensional vector, where the i-th vector component of $D$ corresponds to a term weight $w_i$ of term $t_i \in T$, indicating its importance for $D$.

We will use the previously defined TFIDF score as term weight: $w_i = tfidf(t_i, D)$.

Exercise: implement a function to generate a TFIDF-vector representation for a given document id, based on the the information available in the index. For the purposes of this exercise, implement vectors as lists. Make sure to keep dimensionality between documents, i.e. the same vector dimension should always correspond to the same index term!

In [ ]:
def get_document_representation(doc_id, index):
"""
Returns the tfidf vector for a given doc_id and index
:param doc_id: doc_id to construct the vector for
:param index: index to construct the vector from
:return: the tfidf vector for this document
"""
# Your code here

## Query Representation¶

To retrieve similar documents to a given query, we need to project the query into the same vector space as our document representations.

The query representation is constructed in a similar way to document representations, using the term data stored in the index. However, we calculate the term frequency manually, since a text query, not a document, is indexed. Keep in mind that the query needs to be processed in exactly the same ways as documents, i.e. have the same preprocessing applied.

Exercise: implement a function to generate a TFIDF-vector representation for a text string, based on the the information available in the index. For the purposes of this exercise, implement vectors as lists. Make sure to keep dimensionality between documents, i.e. the same vector dimension should always correspond to the same index term!

In [ ]:
def get_query_representation(text, index):
"""
Returns the tfidf vector for an arbitrary string.
:param text: string to construct the vector for
:param index: index to construct the vector from
:return: the tfidf vector for the string
"""
# Your code here

## Relevance Function¶

Now that we have a way to embed both documents and the query into a common vector space, we can rank documents according to a similarity function with respect to the query.

#### Building the Vector Space¶

To retrieve documents, we need to build a vector space, i.e. construct the representation vector for every document in our collection.

Exercise: construct a vector space for all documents in the index using their document representations. Use a {doc_id: vector, ...} dictionary as data structure.

In [ ]:
# Your code here

#### Defining similarity¶

To calculate the similarity score between the query and each document, we need to define a similarity function. We will use cosine similarity.

Exercise: implement cosine similarity. (Be mindful of the difference between distance and similarity!)

In [ ]:
from math import sqrt, pow

def score(vec_a, vec_b):
# Your code here

#### Querying¶

We now have all the components needed to answer queries. Write a wrapper function that takes a text and returns the (top $k$) results for the query. It construct a query representation and calculate the pairwise similarity between the query and all documents, returning an ordered list of (doc_id, score) tuples, descending by score.

Exercise: write a function to query the vector space.

In [ ]:
def query(text, vectors, index, topK=-1):
"""
Queries a given text against a given vector space. Embeds the query text and calculates the cosine similarity to every document in the vector space.
:param text: query text
:param vectors: list of document vectors to query against
:param index: the index data to query against
:param topK: number of top results to return
:return: list of (doc_id, score) tuples descending by score for all documents in the vector space
"""
# Your code here

# Simple Retrieval¶

You can now try out different queries. There are two example searchers below, but try and search for anything you like. Take a look at both the ranking results as well as the original documents; try to trace why certain documents appear in the order they are in given their TFIDF similarity.

In [ ]:
query("two households verona", vectors, index, topK=5)

In [ ]:
query("love", vectors, index, topK=5)

In [ ]:
# Your code here?


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# Salesforce Application Performance: The OODA Method

, Developer, Performance, Salesforce

A while back I wrote about how I believed Salesforce application performance was an area that needed further investigation to help provide a set of best practices and guidelines to help people write better and more performant applications. One of the things I wanted to do following that post was to share a method that I have used to help me when I am checking the performance of an application, trying to improve it or fixing an exceeded governor limit - OODA. After hitting a performance issue yesterday it was very top of mind so I finally put virtual ink to paper.

## To start - “Premature optimisation is the root of all evil”

I want to begin this by stating I try to improve performance of my applications wherever possible but do not attempt to prematurely optimise. I agree with those like who state that on the platform a certain amount of optimisation is needed inherently, for example bulkification of triggers and grouping of SOQL queries. What I try to avoid though is being overly obscure in my coding to provide a performance improvement when first writing the code. Readable and easy to understand code is unbelievably important and if you have the choice between doing something smart to remove a single query or having your code much easier to read, make your code easier to read. Again this is all an art because there is a lot of grey and very little black and white here, but hopefully you get the drift.

## So what to do when you need to improve performance

Typically this happens when you discover a larger than expected data volume (adding a new country or business group to an org for example), something in the config side of things is having an impact (flow or process builder bulkification for example) or or you are just feeling the application is slower than you would like. Its at this point I break out the OODA method which I became aware of formally whilst learning about Metrics-Driven Development last year but had been using in practice without a name for a while. I was glad I found a name however because it looked a lot better on a slide.

My slide from London’s Calling

OODA is a miltary framework for making decisions (to massively undersell it) and stands for Observe, Orient, Decide and Act. I think it is a great way of working when trying to improve performance and especially when dealing with those lovely “too many queries” errors and governor limit exceptions. I like to use the framework to solve such a problem in the following way.

### Observe

Take measurements, as many relevant ones as possible. When dealing with something like a blown governor limit you can use the System.Limits methods to take snapshot measurements and debug them (or save if you so wish to a record). You should take as many measurements as is sensible and as helps you identify the issue area. It is important as well that measurements are consistent, repeatable and under the same conditions - comparing apples and oranges will not help us later.

### Orient

Now we have our measurements we need to think about what they mean in context. For example, why are we repeatedly running that query? Could this piece of code be avoided through an earlier check? Which area is having the biggest impact and why? Can we reduce the payload? Measurements only tell half the story, here we add the correct context from the business use case and well as looking at the lifecycle of the transaction. We have all come across strange use cases where it becomes clearer why a weird design decision was made.

### Decide

Big questions:

1. Do we fix/improve this? NO is a valid option here and you should be careful to spend time improving things for minor gains.
2. Do we attempt an update or a rewrite?
3. Can part of this be made asynchronous?
4. Are we sure this is the right decision? Is there an alternative way or workaround?

If you are fixing a bug then you may not be able to make some of these decisions - they may already be made.

### Act

Almost the easiest part - make the updates and remeaure and retest. Don’t just retest that you are not getting the error or that things are faster, retest that it still does what you expected.

## Summary

In short OODA is a great way for helping make decisions when performance testing/profiling as well as bug fixing for governor limit exceptions. It helps me out whenever something like this crops up (such as yesterday for me) and provides a solid framework which can help you and your team go through nd make the right decisions.


text:
# How do you simplify 7^-3/8^-4?....Deleted the first of the opening double hash without changing content.

Write as ${8}^{4} / {7}^{3} = \frac{4096}{343} = 11 \frac{323}{343}$


text:
# Resources for title page and front matter design

I need to create the area between the outer cover and the table of contents for a novel. This will present (at least partially, but preferably at a minimum):

• the title
• the author's name
• the translator's name
• the year of first publication
• the name of the book series

I basically need a place to display this information, but (perhaps or preferably) not all crowded into the same page.

Most of the documentation I have read suggests that this is a highly important part of all books and that the book-makers need to creation this part of the book themselves.

So, I am looking for resources which will aid LaTeX book-makers (such as myself) in creating this part of the book. So far, I have found:

Most of the other resources I have seen appear more suited for writers of technical documentation or thesis on A4 paper. I am not sure how well this translates to works of fiction printed on a small size for reading on a park bench. I have found no examples focused on novel-sized material, focusing on use of the book, octavo class or fiction-focused classes, or with styles suitable for works of fiction (either old or new).

I'm looking for at least 1 of these:

• Explanations or links to documents describing the design aspects of title pages and front matter relevant to fiction (or novels in general); old or new methods (any is appropriate).
• Explanations or links to documents describing how to achieve good results between \begin{titlepage} and \end{titlepage} (i.e. achieving proper placement of the elements).
• Links to or samples of source code (either from real works or produced as demonstration code).
• Suggestions for packages, macros, fonts, and other design elements which could benefit users wishing to create title pages and front matter for their works.
• Large or small ideas for how to achieve an excellent-looking title page and front matter with LaTeX (or in general).
-
What's wrong with good old \title, \author, \date and \maketitle? –  Werner Nov 16 '11 at 7:34
That is good, it is just missing: publisher, publisher series, publisher's location, story series, editor, illustrator, copyright information, bibliographical note, cataloging data, manufacturing data, etc. –  Village Nov 16 '11 at 7:47
Okay, then you don't have to use \maketitle; you could just list the items yourself without resorting to some command. Are you using the document items you speak of anywhere else in your document? Do you reference them and therefore need them stored somewhere? –  Werner Nov 16 '11 at 7:50
No, the items only appear once. They are pulled from another file. –  Village Nov 16 '11 at 8:04

http://ctan.org/tex-archive/info/latex-samples/TitlePages This has some great-looking examples, however, the dependencies are all very complicated (i.e. knowing which packages to load in order to compile an example requires familiarity with dozens of packages), and they are also limited to 1 page.

I have taken (some of those examples) in the past and put them as individual examples. You can download these from Here, Here, Here, and Here. I have changed the examples little to work with xepersian package to typeset Persian documents.

-
Vafa Khalighi: sample title page package 3 the link to it in this comment. Excellent job by the way! –  Count Zero Nov 21 '11 at 14:27

Markus Kohm, the author of KOMA-Script, provides a project and a package named titlepage. Unfortunatly the project itself and the download page is only available in German. Nevertheless you may see the different types of already supported title page styles at http://www.komascript.de/node/1219. BTW: The red parts of the example pages are the variant parts. They are only red to illustrate the variant elements.

The package documentation itself is in English. So, if you download the package archive, you get an English manual. Just go to http://www.komascript.de/node/1213 and click at titlepage.tds.zip at the end of the page below the word "Anhang".

You may ask questions about the package and give suggestions for new styles in english too. Nevertheless it would be nice, if the author would put the package onto CTAN, IMHO.

Here is a tiny example in how to use the package:

\documentclass{book}
\usepackage{titlepage}
\TitlePageStyle{Markus-2}% one of several supported styles
\begin{document}
\maketitle[% Note, that this is an option brace!
rulewidth=2pt,% vertical rule at the left
subject=Novel,
title={From here to there},
subtitle={A journey to somewhere},
author={Village},
publisher={Me}
]
\end{document}

Caveat: The titlepage package needs KOMA-Script 3.09a. Nevertheless it may be used together with other classes (see the example above, that uses the standard book class).

-
I do use the KOMA-script and build, almost always, such pieces of a book's meta-data, by using the provided environments (such as: Publishers, Upper- and Lowertitleback, Address and Rightaddress). Fine positioning of certain blocks of text can be achieved by using minipages. However, I second the practice described by Daniel below (answer on Nov 16 at 14:06)--the cover for a novell book can be created outside the LaTeX world and well integrated as a separate PDF page. –  Nikos Alexandris Nov 23 '11 at 9:22
@Nikos: I agree that designing a package or macros for title generation of a one time project wouldn't make sense. But If someone often needs title pages with the same design it would make sense. And if different users need the same design it is useful if one one makes the design and implementation and all the others may use the result. So a project like the titlepage project may make sense for some people and make no sense for others. BTW: Title pages are not same like cover pages! Nevertheless titlepage provides an environment without margins useful for creating covers too. –  Schweinebacke Nov 23 '11 at 9:36
agreed--it certainly will ease off the workflow, given a specific titlepage is required often. –  Nikos Alexandris Nov 25 '11 at 11:28

In answer to your third bullet, you could just create such a title page yourself and not use any other packages. Here is some discussion on how that could be achieved.

The \maketitle command from the article documentclass is defined in the following way:

\newcommand\maketitle{\begin{titlepage}%
\let\footnotesize\small
\let\footnoterule\relax
\let \footnote \thanks
\null\vfil
\vskip 60\p@
\begin{center}%
{\LARGE \@title \par}%
\vskip 3em%
{\large
\lineskip .75em%
\begin{tabular}[t]{c}%
\@author
\end{tabular}\par}%
\vskip 1.5em%
{\large \@date \par}%       % Set date in \large size.
\end{center}\par
\@thanks
\vfil\null
\end{titlepage}%

As you can see, apart from some redefinitions, it leaves a 60pt vertical skip from the top of the page, then typesets the title page information within a center environment. The title (contained within \@title) is typeset in \LARGE font, followed by a vertical skip of 3em, followed by the author (contained within \@author) which is typeset in \large font, followed by the date (in \@date) after a vertical skip of 1.5em, followed by any "thanks" (contained within \@thanks) which is actually typeset as a \footnote. You could mimic this procedure almost verbatim using the titlepage environment:

\begin{titlepage}
\null\vfil
\vskip 60pt
\begin{center}
{\LARGE My novel title \par}%
\vskip 3em
{\large
\lineskip .75em%
Author: Random Randofsky \par
Publisher: Random Pub \par
Publisher series: XyZ \par
Publisher location: Random City \par
Story series: aBc \par
Editor: Who Cares \par
Illustrator: Someone Special \par
Bibliographical note: \biblatex \par
Manufacturing data: whatever \par}%
\vskip 1.5em%
{\large \today \par}% Set date in \large size
\end{center}\par
\vfil\null
\end{titlepage}

The layout, of course, would depend on the contents of the respective elements you want to include. I've just used filler text to display something.

If need be, it would also be possible to create a number of macros where you define the respective items, and then call a "title page" macro that assembles everything into the above format (for consistency). However, more information regarding the layout would be required to establish such a definition.

-

A prosaic approach (that probably does not go too well with many here at TeX.SE):

If this is just a one-time thing then do not mess with LaTeX at all to do the cover. Just do it in your favorite vector drawing program (such as Inkscape), export it to PDF, and use something like pdfpages, \includegraphics or pdftk to add it to the document. Especially if you need a more arty design, such as for a novell or poetry book, this can be a huge time saver (although doing it with TikZ might be fun).

On the other hand: if it is something you (or someone else) may want to do more than once and the format is pretty formal, then you should invest the time in doing it with LaTeX.

-
I couldn't agree more with the sentiment here. The cover and the title pages will define the readers first impression of your book and should therefore be designed to best suit it. No standard setup exist as every book is unique, which is especially true for novels and prose in general. Browse your bookshelves for inspiration and I'm sure TeX.SE will help you create what you desire in TikZ, if you so choose :) –  spet Nov 21 '11 at 9:22


text:
# Why are salient pole rotors preferred in hydro plants?

Hi all,

I tried to post in this post https://www.physicsforums.com/threads/salient-and-non-salient-pole-synchronous-generator.878198/ but I now realise that creating a new thread might have been better.

So...
• Salient rotors are not used in high rotational speed applications, and we must use cylindrical rotors due to mechanical reasons, OK I get that.

• Why are salient rotors the "preferred choice" at low speed applications, such as in hydro power plants? What are the advantages of salient rotors (electrical and/or mechanical), since hydro power plants use salient rotors over cylindrical rotors at low speed applications?
• Are there any benefits of having a non-uniform air gap compared to having an uniform air gap, and hence uniform flux distribution(?)?

Best regards

## Answers and Replies

If you want to make 60 Hz power (or 50 Hz), with a low speed generator, it takes many, many poles. The construction of so many poles on a round rotor would be very difficult to get enough turns on each pole. Look at a round rotor and see how the turns are laid into the surface of the rotor. Commercial generators almost always use 3600 rpm (or 3000 rpm) with a two pole rotor. Now imagine trying to wind perhaps 20 poles on a round rotor.

LagCompensator, Bavuka and jim hardy
jim hardy
Gold Member
Dearly Missed
Back to basics:

Voltage is in proportion to relative velocity between the conductor and the magnetic field.
In a slow turning water turbine it takes huge diameter to get much velocity.

I think you'd rather assemble this from separate pieces than machine it out of a solid forging.


text:
# Issue with multithreading and standard output

I have a multithreaded piece of python code that moves the arms of my robot. The basic premise is that there is one thread for each arm, and threads block until each arm as finished it's movements (i.e., given two sets of joint positions, one for each arm, the program splits into two threads that loop until their respective arm has reached the specified joint positions). Here is the code that does that:

def __moveToJointPos(self, instance, index): if instance >= self.numInstances(): raise Exception("Called with instance " + str(instance) + " but only " + str(self.numInstances()) + " instances exist")

    t = None
if type(index) is tuple:
#If this method is being called with 2 indices rather than one, that means we want to move both arms at the same time.
#To do this, we spin off one of the indices to another thread, then execute as normal on the remaining one.
#Then we wait until the other thread finishes before returning.
if len(index) > 2:
raise Exception("Can only call with a tuple of size 2, got a tuple of size " + str(len(index)))
elif self.poss[instance][1][index[0]][0] == self.poss[instance][1][index[1]][0]:
raise Exception("When calling with a tuple, must specify indices with different arms.")
elif len(index) == 2:
i2 = index[1]
t.daemon = True
t.start()
mov = self.poss[instance][1][index[0]]
else:
mov = self.poss[instance][1][index]

rate = rospy.Rate(10)

if mov[0] == Behavior.RIGHT_ARM:
arm = self.right_arm
else:
arm = self.left_arm
done = False
dd = [9999.0, 9999.0, 9999.0, 9999.0, 9999.0]
while not done:
arm.set_joint_positions(mov[1])
dist = 0.0
for j in arm.joint_names():
dist = dist + (mov[1][j] - arm.joint_angle(j))*(mov[1][j] - arm.joint_angle(j))
dist = math.sqrt(dist)
ss = 0.0
for d in dd:
ss = ss + math.fabs(d - dist)
if ss < 0.01:
done = True
elif rospy.is_shutdown():
print("ROS shutdown, cancelled movement")
done = True
if baxter_external_devices.getch() in ['\x1b', '\x03']:
print("stopped")
done = True
else:
dd.append(dist)
del dd[0]
rate.sleep()

if t is not None:
t.join()

I'll admit the code is rather messy, but this is just something I'm quickly hacking together to test out the robot. Here is the code that calls that function:

     print("a")
self._Behavior__moveToJointPos(0,(ToTable.lHOME, ToTable.rHOME))
print("b")
self._Behavior__moveToJointPos(0,(ToTable.lMID, ToTable.rMID))
print("c")
self._Behavior__moveToJointPos(0,(ToTable.lTABLE, ToTable.rTABLE))
print("d")

(the prints are added so that the effect on standard out is more clear). Here is what my terminal looks like:

Here is the link to the image: http://i.imgur.com/1hdCq7f.png

(you may need to open it in a separate tab to see it). There are a couple more calls to __moveToJointPos, which is why there is more text output, but the error starts with the set of commands above. As you can see ...

edit retag close merge delete

Sort by » oldest newest most voted

It looks like you're accidentally sending some kind of control code to the terminal subsystem that's disabling the local echo and carriage returns.

For starters, you should be able to reset your terminal to the default state with the stty sane command (hit enter, type and pray).

Beyond that, I would inspect your program's print statements for stray escape sequences that could be causing this. If you don't find anything obvious there, you could try piping the output through something like hexdump to decode all of the console output before is passes into the pseudo-tty layer and messes things up.

Go read "Advanced Programming in the UNIX Environment" or another similar UNIX systems programming book for more details of the underlying mechanics here.

more

Thanks for the help. stty sane worked beautifully. I don't really have time at the moment to parse through the output and figure out exactly what is happening, so for the moment I just hacked it and added 'call(["stty", "sane"])' in the last if block right after 't.join()'. It works for now, I'll fix it later. Thanks again!

( 2014-02-11 07:25:35 -0500 )edit


text:
I’ve just uploaded to the arXiv my paper “Global regularity of wave maps VI.  Abstract theory of minimal-energy blowup solutions“, to be submitted with the rest of the “heatwave” project to establish global regularity (and scattering) for energy-critical wave maps into hyperbolic space.  Initially, this paper was intended to cap off the project by showing that if global regularity failed, then a special minimal energy blowup solution must exist, which enjoys a certain almost periodicity property modulo the symmetries of the equation.  However, the argument was more technical than I anticipated, and so I am splitting the paper into a relatively short high-level paper (this one) that reduces the problem to four smaller propositions, and a much longer technical paper which establishes those propositions, by developing a substantial amount of perturbation theory for wave maps.  I am pretty sure though that this process will not iterate any further, and paper VII will be my final paper in this series (and which I hope to finish by the end of this summer).  It is also worth noting that a number of papers establishing similar results (though with slightly different hypotheses and conclusions) will shortly appear by Sterbenz-Tataru and Krieger-Schlag.

Almost periodic minimal energy blowup solutions have been constructed for a variety of critical equations, such as the nonlinear Schrodinger equation (NLS) and the nonlinear wave equation (NLW).  The formal definition of almost periodicity is that the orbit of the solution $u$ stays in a precompact subset of the energy space once one quotients out by the non-compact symmetries of the equation (namely, translation and dilation).   Another (more informal) way of saying this is that for every time $t$, there exists a position $x(t)$ and a frequency $N(t)$ such that the solution $u(t)$ is localised in space in the region $\{ x: x = x(t) + O(N(t)^{-1}) \}$ and in frequency in the region $\{ \xi: |\xi| \sim N(t) \}$, with the solution decaying in energy away from these regions of space and frequency.  Model examples of almost periodic solutions include traveling waves (in which N(t) is fixed, and x(t) moves at constant velocity) and self-similar solutions (in which x(t) is fixed, and N(t) blows up in finite time at some power law rate).

Intuitively, the reason almost periodic minimal energy blowup solutions ought to exist in the absence of global regularity is as follows.  It is known (for any of the equations mentioned above) that global regularity (and scattering) holds at sufficiently small energies.  Thus, if global regularity fails at high energies, there must exist a critical energy $E_{crit}$, below which solutions exist globally (and obey scattering bounds), and above which solutions can blow up.

Now consider a solution $u$ at the critical energy which blows up (actually, for technical reasons, we instead consider a sequence of solutions approaching this critical energy which come increasingly close to blowing up, but let’s ignore this for now).  We claim that this solution must be localised in both space and frequency at every time, thus giving the desired almost periodic minimal energy blowup solution.  Indeed, suppose $u(t)$ is not localised in frequency at some time t; then one can decompose $u(t)$ into a high frequency component $u_{hi}(t)$ and a low frequency component $u_{lo}(t)$, both of which have strictly smaller energy than $E_{crit}$, and which are widely separated from each other in frequency space.  By hypothesis, each of $u_{hi}$ and $u_{lo}$ can then be extended to global solutions, which should remain widely separated in frequency (because the linear analogues of these equations are constant-coefficient and thus preserve frequency support).   Assuming that interactions between very high and very low frequencies are negligible, this implies that the superposition $u_{hi}+u_{lo}$ approximately obeys the nonlinear equation; with a suitable perturbation theory, this implies that $u_{hi}+u_{lo}$ is close to $u$.  But then $u$ is not blowing up, a contradiction.   The situation with spatial localisation is similar, but is somewhat more complicated due to the fact that spatial support, in contrast to frequency support, is not preserved by the linear evolution, let alone the nonlinear evolution.

As mentioned before, this type of scheme has been successfully implemented on a number of equations such as NLS and NLW.  However, there are two main obstacles in establishing it for wave maps.  The first is that the wave maps equation is not a scalar equation: the unknown field takes values in a target manifold (specifically, in a hyperbolic space) rather than in a Euclidean space.  As a consequence, it is not obvious how one would perform operations such as “decompose the solution into low frequency and high frequency components”, or the inverse operation “superimpose the low frequency and high frequency components to reconstitute the solution”.  Another way of viewing the problem is that the various component fields of the solution have to obey a number of important compatibility conditions which can be disrupted by an overly simple-minded approach to decomposition or reconstitution of solutions.

The second problem is that the interaction between very high and very low frequencies for wave maps turns out to not be entirely negligible: the high frequencies do have a negligible impact on the evolution of the low frequencies, but the low frequencies can “rotate” the high frequencies by acting as a sort of magnetic field (or more precisely, a connection) for the evolution of those high frequencies.  So the combined evolution of the high and low frequencies is not well approximated by a naive superposition of the separate evolutions of these frequency components.

There are a number of ways to resolve the first problem.  One way, which has been pursued in a very recent paper by Sterbenz and Tataru (and also in an earlier paper of Tataru, and of myself in the case of spherical targets), is to embed the target manifold into Euclidean space and perform various operations (e.g. Littlewood-Paley projections) on the solution in that ambient space, thus creating new fields which lie outside the target.  This does not work directly with the hyperbolic space target because this is not efficiently embeddable into Euclidean space (although it was recently pointed out to me by Jacob Sterbenz that one can proceed – at least for the narrow question of establishing global regularity rather than scattering – by passing from hyperbolic space to a compact quotient).  Another approach, introduced by Krieger, is that of dynamic separation – to isolate a “dynamic” scalar field which is unconstrained, controls all the other components of the evolution (as “static” functions of the dynamic field), and then manipulate the dynamic field directly.  It is this latter approach which we will pursue in the sequel to this paper; the dynamic field we will use is the tension field $\psi_s$ of the harmonic map heat flow.

For the second problem, we will use a variant of the “frequency truncation method” of Bourgain, constructing the solution iteratively, in a sequence of time intervals in which the low frequency solution is small in a certain spacetime norm sense.   On each such time interval, the impact of the low frequencies on the high ones is small enough that one can basically ignore the low frequencies, and evolve the high frequencies using the hypothesis that solutions with energy less than $E_{crit}$ have global solutions.  But then one has to appeal to the hypothesis again at every time interval, otherwise the cumulative effect of the low frequencies on the high frequencies will become uncontrollable.  This is not a problem unless the energy of the high frequencies increases significantly after every time interval.  But one can use the energy conservation of the low frequencies and of the entire solution to prevent this from occuring.

All of these things will be detailed in the sequel to the current paper.   What the current paper does is to perform the abstract argument that constructs minimal-energy blowup solutions, assuming four black-box results which will be proven in the sequel:

1. A perturbation theory for wave maps which enjoys a certain fungibility property, which is technical to state but roughly asserts that any large wave map on a long time interval can be subdivided into a controlled number of shorter time intervals in which the evolution behaves like the linear equation;
2. A means of synthesising solutions from frequency-delocalised data from solutions at strictly lower energies;
3. A means of synthesising solutions from spatially-dispersed data from solutions at strictly lower energies;
4. A means of synthesising solutions from spatially-delocalised data from solutions at strictly lower energies.

(Here, “spatially dispersed” means, roughly, that the energy density does not accumulate at any point, while “spatially delocalised” means that there is a location where the energy density accumulates, but a significant amount of energy is also present at a large distance from this accumulation point.  These two scenarios complement the scenario we actually want, which is spatial localisation – where the energy density accumulates at one point and decays away from that point.)

The abstract component of the argument is in fact quite similar to that used for the energy-critical NLS by Colliander, Keel, Staffilani, Takaoka, and myself.  There are also some more concrete components to the argument in this paper, though, namely the use of the harmonic map heat flow as a kind of nonlinear Littlewood-Paley resolution in order to formally define frequency delocalisation and set up its basic properties, and also a Rellich-type compactness lemma which asserts that solutions which are localised in space and frequency are indeed almost precompact, and which is also proven using the harmonic map heat flow.


text:
# Questions tagged [pid]

Proportional Integral Derivative Controller. A type of control algorithm used in many control situations, especially servo systems.

314 questions
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20 views

### PID controller for slowly varying system [duplicate]

I am making a robot that is required to move in a straight line, but it is slowly turning on the left or right, this error keeps accumulating (eventually resulting in a very large radius turn). So, ...
1 vote
80 views

### Impact of using PID Output as a Change (Delta) vs Absolute

I am trying to control speed of a motor using PID. It seems like I have two approaches. Using PID to calculate the absolute duty cycle value of the PWM Using PID to calculate the change needed in the ...
• 111
1 vote
124 views

### How to use a PID controller for different kinematics robots

I implement different drive odometry for a robot. Trying to implement (proportional–integral–derivative controller) PID-based coordinate movements x, y, theta: ...
• 13
53 views

For a project I am building and programming my own flight controller. I have seen the implementation of a single loop PID controller. But after doing some more research I've found that a cascading PID ...
41 views

### How to Contol the RPM of a Micro Metal Gearmotor with Encoders (Pololu) using PID?

I use the PID algorithm to control the RPM of a micro Gearmotor. My motor and encoder specifications are given below. Motor: https://www.pololu.com/product/2378 - 6V 29.86:1 gear ratio - please ...
• 121
47 views

### How is named a controller that sets a position to reach with a constant velocity?

I looked everywhere I could but didn't find a useful answer, so let me explain here: My controller is giving a position goal, and while this position is not achieved, the linear actuator is controlled ...
1 vote
78 views

### Differential Drive Control Techniques

I have a mobile robot that has a differential drive technique. I try to control the robot with PID controller. Is the best way for controlling differential drive robots? If I want to compare different ...
• 21
57 views

### control of a rod attached to a motor

I have a 76 cm, aluminum rod, attached to the shaft of a 12v DC banebot motor. The rod is hanging vertically initially, and rotates in the vertical plane. The task is to control the rod to make it ...
• 111
1 vote
64 views

### How to avoid oscillations caused by backlash in position control?

I am working with a ball screw mechanism driven by a brushless dc motor with an encoder mounted on the load side. We are using a PID position controller with tuning settings by optimization however ...
38 views

### Center line steering with differential drive

I’ve got 2 motors that drives my unit and I can easily steer it manually by simply adding more speed to one wheel vs the other. Now I’m automating the rover using image processing to follow a driveway....
• 23
19 views

### Detailed resources for control of linear actuators including backlash/friction compansation and controller design?

I am working on a project where I would like to control a linear actuator with a ball screw mechanism. I feel I need a reference book for position/servo control systems for dc motors as there are many ...
39 views

### The math behind minimum controller sample rate compared to actual error frequency spectrum

It seems intuitive to me that, in a digital system, a system sampling the error rate "too slowly" will fail to stabilize the system. Is there a theory/set of metrics/equation I can use to ...
28 views

### Strategies for tuning with low sample rate

I’m designing an arduino robot that’s objective is to find and drive towards a light using a photo resistor mounted on a servo. I want to write my program with PID control to sweep the photo-resistor ...
159 views

### How do I find the transfer function for my quadcopter altitude system?

This is not so much of a how but if I am right so far. I am looking at the z-axis now only. The linearized equation of motion for the thrust in the z-direction is: $$T=m\cdot \ddot{z}+mg,$$ where $m$...
77 views

### Outer Position Loop to Control Inner Velocity Loop

I'm trying to control the position of a brushless DC gearmotor. To drive the motor, I have a controller box that provides a velocity that is proportional to a 0 to 5 V input. The motor has it's own ...
• 109
1 vote
47 views

### PID control for robotic manipulator servoing

I'm trying to enable robotic manipulator servoing using MoveIt servo implementation. However, I'm having some questions regarding reference following and error compensation. The thing is, I roughly ...
333 views

### Self balancing bike using a flywheel: ROS implementation

I have a bike with two stands and a flywheel like this: The stands can be adjusted so that they don't touch the ground. Now, the task is to implement a self balancing mechanism: when I run the script,...
• 111
324 views

### Implementing PID on a line following bot using turtlebot

I am using ROS melodic,turtlebot 2 on Ubuntu 18.04. The idea is to create an environment consisting of lines as a path (slightly curved), and to program the turtlebot to follow the lines. Basically, a ...
• 111
64 views

### Mapping Joystick Inputs to Quadcopter

hope you are all doing well. We are doing a project where a quadcopter is controlled by an ordinary joystick. We have constructed the Control Algorithm and the joystick to move the quadcopter in ...
• 306
72 views

### Bug in code of Self-Balancing Bot

I am making a Self balancing bot as my project in which I am using MPU6050, Arduino Uno, motor driver l298n and DC motors. I am making this using data from accelerometer and gyroscope and combining ...
38 views

### PI controller for skew angle on a train wagon like robot

I have a robot very similar to a train wagon, it has 4 actuated wheels controlled by 2 motors. The two wheels that are located on the same rail are controlled by the same motor. On each wheel it's ...
• 33
53 views

### Identifying active PID-Controller parameters

A metric of a physical system is being controlled by a PID controller (in this case a valve controls the temperature of a liquid by mixing hot liquid into a stream of cold liquid). All measurement ...
• 101
94 views

### Rotate a certain angle using PID and mpu6050

Currently I'm working with a 4 wheel robot and I'm trying to rotate a certain amount of angle. I used PID_V1 library to rotate this. But when I upload and test the code Robot rotate continously. ...
75 views

### How to design a PID controller for boat?

I have a boat with two trusters and a trajectory planner which is based on the bicycle model. In order to control the boat, the linear velocity of each truster has to be provided. The following ...
• 125
69 views

### Robots Following Robots with Safety Distance Planning and Coordination

I have two robots, I wish for the second robot to follow the first one while keeping a constant distance d_safe between them. I am trying to implement a PID ...
• 115
56 views

### Find viscous friction for DC motor transfer function

How do I find the viscous friction for my DC motor without measuring the input current and output torque. I have to do a theoretical model on simulink and can't find any answers on how to find it
1 vote
111 views

### How to implement PID position control for 4wheel mecanum robot?

I want to implement PID control on my 4 wheel mecanun robot. I want to give a position instruction to my robot and that it follow the following curves of velocity and position. The only feedback that ...
• 11
87 views

### Inner current controller benefits

I am currently working on a system with a BLDC motor attached to a non linear spring on which a user can apply a force. Meaning the torque applied on the motor's output is most of the time unknown. ...
• 31
1 vote
83 views

### How to choose closest angle when crossing -180 degrees

I'm applying a PID for position control on a diff drive robot, got the angles (orientation )between -pi and pi. It works fine until it needs to change its orientation from (let's say) -170 degrees to ...
257 views

### PID controller for motor speed control and distance control

I am building a robot rover comprised of dual DC motors each with hall sensors to obtain rotaional speed. I currently have a PID controller for each DC motor that is able to control the speed of the ...
• 91
37 views

### How to prove the stability of trajectory tracking with PD control using Lyapunov method?

I'm having a problem to prove the stability of PD control in trajectory tracking. Let say we have a system with double integrator dynamics and we what to minimalize the tracking error $\tilde{x}$. ...
• 87
51 views

### Quadcopter descends when rolled or pitched

I'm currently working on a quadcopter using f450 frame and YMF32 code. I was able to successfully build the quadcopter and It flies without having any vibrations or wobbles. Also, I tuned the PID ...
179 views

...
124 views

### PID Control: Is adding a delay before the next loop a good idea?

I am implementing PID control in c++ to make a differential drive robot turn an accurate number of degrees, but I am having many issues. Exiting control loop early due to fast loop runtime If the ...
100 views

### Can I measure torque from this motor by only measuring the current?

I am new to robotics, please forgive/correct any errors. My Project Plan I want to use a PID controlled motor in a human-interface device where I need to measure the user's exerted force on an end ...
• 123
1k views

### PID controller that targets a set rotation and a set velocity at that rotation?

I have a 3d physics simulation where I use a PID controller to reach a set orientation (orientation error drives a torque output). Which works well enough some cases, but in others it's not working ...
• 123
121 views

### pid tuning the wheel velocity

I am using diff drive controller to control the wheels of my robot. Here i am trying to use the control toolbox pid class for making the input velocity and velocity measured from wheel encoder to be ...
• 121
91 views

### High derivative gain in PD control

Why does high derivative gain in PD control results in motor noise or chatter? The graph that I see on MATLAB simulation is smooth enough, so following that it should not make noise..
50 views

### What is the difference between The state-space equation and The configuration-space equation

The craig(p.180) states that equations can be made to represent the dynamic equations. The first one being the state space equation. \$\tau=M(\Theta)\cdot\ddot{\Theta} + V(\Theta,\dot{\Theta}) + G(\...
72 views

### Reliably enabling/disabling a PID loop via FSM in a microcontroller

I have a PID loop for a small vehicle implemented in a microcontroller. Currently the PID loop is implemented in a timer interrupt. I want to implement an FSM that will have states that enable or ...
• 101
199 views

### Motion profile and Motion control scheme, how do they interact?

I'm studying motion control and I start with the simplest case, I have to go from A to B in a straight line using a trapezoidal motion profile. I understand that in a real case, due to the fact that ...
• 33
1 vote
305 views

### To calculate roll,pitch and yaw

How do I calculate roll,pitch and yaw value from the position co ordinates of the drone, that is x,y and z from the gps sensor??? Using the x,y and z co ordinates I have to calculate roll,pitch and ...
1 vote
41 views

### How to compensate for back drive caused by gravity

I have a 24v DC motor with a planetary gear box, Hbridge, and encoder feedback that drives an arduino robot similar to a winch that moves a weight by spooling a strap up and down. The problem I am ...
1 vote
258 views

### Quadcopter PID Controller for distance

I am trying to use a PID controller to stop a quadcopter at a specific location while travelling horizontally, however currently it overshoots/undershoots depending on the max velocity. I have tried ...
• 121
67 views

### Res-Scaling method beats PID controller. How?

Scenario: I have a robotic arm that has a (1D) lidar on its end, to orient itself with respect to the slant table in front of it. The lidar returns pretty accurate distance values in mm. The motor ...
• 133
109 views

### Imaginary part in result of inverse laplace transform

I am working with a system(closed-loop feedback control) that has a transfer function like this F = 20*(s+5)/(s^4+13.5s^3+41s^2+80*s+100) this one is in the s-domain but for the response analysis, I ...
97 views

### Finding the right PD values for a quadcopter simulator

I am working on this short assignment where I have to find the right PD values for a simulated quadcopter. I have to reach 0.9 meters under 1 second with an overshoot of less than 5%. This is my ...
• 111
1 vote
84 views

### PID on DC motor turning on both directions

I have a skid steer robot where I have four individual DC motors with an H bridge so I can control speed and direction. There are also four quadrature encoders with 6000 ticks per revolution. The ...
• 11
1 vote


text:
# The leg of a right triangle that lies on one ray of angle θ is called the ___ leg, and the leg that lies across triangle from θ is called the ___ leg.

Right triangles and trigonometry
The leg of a right triangle that lies on one ray of angle $$\theta$$ is called the ? leg, and the leg that lies across triangle from $$\theta$$ is called the ? leg.
The leg of a right triangle that lies on one ray of angle $$\theta$$ is called the adjacent leg, and the leg that lies across triangle from $$\theta$$ is called the opposite leg.


text:
# How do I create a triangulated surface from points?

I have a set of points in a nx3 matrix and I would like to convert them into a surface, so that I may calculate its surface area.

The function ListSurfacePlot3D creates the surface how I want it. How do I compute the surface area from there?

I have tried other functions, such as DelaunayMesh. However, DelaunayMesh creates a closed region defining a volume, causing the surface area to be greater than expected. Which function do I use? If this surface is created correctly, I would use RegionMeasure to get the area.

Edit: Here is my set of data points https://www.dropbox.com/s/db79ewahx24it3r/Data.txt?dl=0

Using Geomagic Control allows me to get the area of the wrapped points, at about 11522 mm2. I don't need the visual, I only want the area from these points.

I'll be running the area calculation through a routine of about 6000 samples.

• See DiscretizeGraphics and TriangulateMesh. You should also provide a sample data if you want people to pay attention and provide help. – RunnyKine Jun 17 '15 at 22:34
• I have added a sample of my data. It appears triangulate mesh only triangulates an existing surface, so I couldn't use that. – Symphos Jun 18 '15 at 15:59

It turns out ListSurfacePlot3D does a terribly poor job of approximating the surface in the OP, otherwise one will just apply DiscretizeGraphics to the output obtained from ListSurfacePlot3D and be done with it. But since that's not applicable here, we present an approach that uses alpha shapes to approximate the shape of the given point set by tuning a parameter. First a helper function for computing the circum-radius of a tetrahedron (we Compile it and give it the Listable Attribute for speed gains):

circumRadius =
Compile[{{v, _Real, 2}},
With[{a = v[[1]] - v[[4]], b = v[[2]] - v[[4]], c = v[[3]] - v[[4]]},
With[{a1 = Plus @@ (a^2), b1 = Plus @@ (b^2), c1 = Plus @@ (c^2),
α1 = b[[2]] c[[3]] - b[[3]] c[[2]],
α2 = b[[3]] c[[1]] - b[[1]] c[[3]],
α3 = b[[1]] c[[2]] - b[[2]] c[[1]],
β1 = c[[2]] a[[3]] - c[[3]] a[[2]],
β2 = c[[3]] a[[1]] - c[[1]] a[[3]],
β3 = c[[1]] a[[2]] - c[[2]] a[[1]],
γ1 = a[[2]] b[[3]] - a[[3]] b[[2]],
γ2 = a[[3]] b[[1]] - a[[1]] b[[3]],
γ3 = a[[1]] b[[2]] - a[[2]] b[[1]]},
Norm[a1 {α1, α2, α3} + b1 {β1, β2, β3} + c1 {γ1, γ2, γ3}] /
(2 Norm[Plus @@ (a[[1 ;; 3]] {α1, α2, α3})])]
],
CompilationTarget -> "C", RuntimeOptions -> "Speed",
RuntimeAttributes -> {Listable}, Parallelization -> True]

And now the code to compute the alpha shape:

alphaShapes[points_, crit_] :=
Module[{alphacriteria, del = Quiet @ DelaunayMesh @ points, tetras,
Pick[tetrahedra, UnitStep @ Subtract[rmax, radii], 1];
selectExternalFaces[facets_] := MeshRegion[points, facets];
tetradii = Quiet@circumRadius@tetcoords /. ComplexInfinity -> $MaxMachineNumber; selectExternalFaces @ alphacriteria[tetras, tetradii, crit] ] ]  For the plot, setting crit to$45$seems to do a good job, but there appear to be holes in the surface. The area appears to be close to the value posted by OP from Geomagic. reg = RegionBoundary @ alphaShapes[data, 45]; (* data is your nx3 matrix *) HighlightMesh[reg, {Style[2, FaceForm[None]], Style[1, Darker@Green]}]  Here is the approximate area: 0.5 Area @ reg  11612. Which is very close to 11522 (the value provided by the OP). Note that I'm dividing the total area by$2\$ since the Area function will compute the areas of the cells on both sides of the image.
• Unfortunately, ListSurfacePlot3D does a pretty poor job of approximating this surface. Try running Show[ListSurfacePlot3D[data], ListPointPlot3D[data]] to see how bad. – Michael Seifert Jun 18 '15 at 16:25


text:
# How to show $\lim_{x \to 1} \frac{x + x^2 + \dots + x^n – n}{x – 1} = \frac{n(n + 1)}{2}$?

I am able to evaluate the limit $$\lim_{x \to 1} \frac{x + x^2 + \dots + x^n – n}{x – 1} = \frac{n(n + 1)}{2}$$ for a given $n$ using l’Hôspital’s (Bernoulli’s) rule.

The problem is I don’t quite like the solution, as it depends on such a heavy weaponry. A limit this simple, should easily be evaluable using some clever idea. Here is a list of what I tried:

• Substitute $y = x – 1$. This leads nowhere, I think.
• Find the Taylor polynomial. Makes no sense, it is a polynomial.
• Divide by major term. Dividing by $x$ got me nowhere.
• Find the value $f(x)$ at $x = 1$ directly. I cannot as the function is not defined at $x = 1$.
• Simplify the expression. I do not see how I could.
• Using l’Hôspital’s (Bernoulli’s) rule. Works, but I do not quite like it.

If somebody sees a simple way, please do let me know.

Added later: The approach proposed by Sami Ben Romdhane is universal as asmeurer pointed out. Examples of another limits that can be easily solved this way:

• $\lim_{x \to 0} \frac{\sqrt[m]{1 + ax} – \sqrt[n]{1 + bx}}{x}$ where $m, n \in \mathbb{N}$ and $a, b \in \mathbb{R}$ are given, or
• $\lim_{x \to 0} \frac{\arctan(1 + x) – \arctan(1 – x)}{x}$.

It sems that all limits in the form $\lim_{x \to a} \frac{f(x)}{x – a}$ where $a \in \mathbb{R}$, $f(a) = 0$ and for which $\exists f'(a)$, can be evaluated this way, which is as fast as finding $f’$ and calculating $f'(a)$.

This adds a very useful tool into my calculus toolbox: Some limits can be evaluated easily using derivatives if one looks for $f(a) = 0$, without the l’Hôspital’s rule. I have not seen this in widespread use; I propose we call this Sami’s rule :).

$$f(x)=x+x^2+\cdots+x^n-n$$
$$\lim_{x \to 1} \frac{x + x^2 + \dots + x^n – n}{x – 1}= \lim_{x \to 1}\frac{f(x)-f(1)}{x – 1}=f'(1)\\[10pt] = \left[ \vphantom{\frac11} 1 + 2x + 3x^2 + \cdots + nx^{n-1} \right]_{x=1} = \frac{n(n + 1)}{2}$$


text:
, 18.10.2019 06:00, Simrankanojia

# The radii of two cylinders are in the ratio 3 : 5 and their heights are in the ratio 2 : 3. what is the ratio of their curved surface areas?

### Other questions on the subject: Math

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If the age of a and b are added to twice the age of s, the total becomes 60. if the age of s and b are added to thrice the age of a, the total becomes 68. if the sum of twice the ages s and b and thrice the age of a is 100. what is the sum of ages of a and b?
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The mid points of the sides of a triangle are (6,1)


text:
# How do you write y=-3(x-3)(x+2)?

$y = - 3 {x}^{2} + 15 x - 18$
$y = - 3 \left(x - 3\right) \left(x + 2\right)$
$\therefore y = - 3 \left({x}^{2} - 5 x + 6\right)$
$\therefore y = - 3 {x}^{2} + 15 x - 18$


text:
# Taking Limits Under the Integral Sign

by F. Cunningham Jr. (Bryn Mawr College)

Year of Award: 1968

Publication Information: Mathematics Magazine, vol. 40, 1967, pp. 179-186

Summary: The author proves that if a sequence of Riemann integrable functions $\{f_n\}$ on $[a,b]$ converges pointwise on $[a,b]$ to a Riemann integrable function $f$ and if the functions $\{f_n\}$ are all bounded by a constant $K$ on $[a,b]$, then the limit of the integrals of the functions $f_n$ over [a,b] is the integral of the function $f$ over $[a,b]$.

About the Author: (from Mathematics Magazine, vol. 40, (1967)) Frederick Cunningham, Jr. was at Bryn Mawr College at the time of publication.

Subject classification(s): Calculus | Single Variable Calculus | Integration
Publication Date:
Wednesday, September 24, 2008


text:
# Math Help - use the partial fraction method to solve 1

1. ## use the partial fraction method to solve 1

dy/dt= 0.5(y^2)-2y where y=0 for x=0

2. Originally Posted by fastman390
dy/dt= 0.5(y^2)-2y where y=0 for x=0
$\int\frac{dy}{y^2- 4y}= \int 0.5 dx$
$y^2- 4y= y(y-4)$ so you can do the left side by "partial fractions" as your title says.


text:
# eigenvectors

• Nov 15th 2008, 03:38 PM
ArTiCK
eigenvectors
Hi all,

For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

First i found the eigenvalues by letting det(A- lamba*I) = 0....
the eigenvalue is lamda = 1

I then solve for my eigenvector

(A - I)v = 0

i row reduce (A - I) to [0 2; 0 0]

Now i am stuck... i don't know how to get my eigenvector

ArTiCk
• Nov 15th 2008, 06:24 PM
Rapha
Hi there

Quote:

Originally Posted by ArTiCK
Hi all,

For the matrix A = [1 2; 0 1], how many linearly independent eigenvector are there?

First i found the eigenvalues by letting det(A- lamba*I) = 0....
the eigenvalue is lamda = 1

I then solve for my eigenvector

(A - I)v = 0

i row reduce (A - I) to [0 2; 0 0]

$\begin{pmatrix} 0 & 2 \\ 0 & 0 \end{pmatrix}$

means, that you have to solve 2 equations

0*x+2*y = 0

0*x+2*y = 0

=> y = 0 and any x

x=1, x= 3 , x= - 10....

$\begin{pmatrix} x \\ 0 \end{pmatrix}$ is eigenvector
and they are linearly dependent,....


text:
# Properties

 Label 5.3.al_ch_ahw_tt_abml Base Field $\F_{3}$ Dimension $5$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{3}$ Dimension: $5$ L-polynomial: $( 1 - 3 x + 3 x^{2} )^{3}( 1 - 2 x + 5 x^{2} - 6 x^{3} + 9 x^{4} )$ Frobenius angles: $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.166666666667$, $\pm0.254551732336$, $\pm0.538152604671$ Angle rank: $2$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 7 55223 19054336 4974322171 1376596978337 269372824813568 52353414280000883 12138856505398324611 2966149666575644571904 712088368727173824104663

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -7 7 32 111 363 928 2289 6551 19760 58567

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{3}$
 The isogeny class factors as 1.3.ad 3 $\times$ 2.3.ac_f and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.3.ad 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-3})$$$)$ 2.3.ac_f : 4.0.4672.2.
Endomorphism algebra over $\overline{\F}_{3}$
 The base change of $A$ to $\F_{3^{6}}$ is 1.729.cc 3 $\times$ 2.729.bk_bww. The endomorphism algebra for each factor is: 1.729.cc 3 : $\mathrm{M}_{3}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $3$ and $\infty$. 2.729.bk_bww : 4.0.4672.2.
All geometric endomorphisms are defined over $\F_{3^{6}}$.
Remainder of endomorphism lattice by field
• Endomorphism algebra over $\F_{3^{2}}$  The base change of $A$ to $\F_{3^{2}}$ is 1.9.ad 3 $\times$ 2.9.g_t. The endomorphism algebra for each factor is: 1.9.ad 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-3})$$$)$ 2.9.g_t : 4.0.4672.2.
• Endomorphism algebra over $\F_{3^{3}}$  The base change of $A$ to $\F_{3^{3}}$ is 1.27.a 3 $\times$ 2.27.e_ba. The endomorphism algebra for each factor is: 1.27.a 3 : $\mathrm{M}_{3}($$$\Q(\sqrt{-3})$$$)$ 2.27.e_ba : 4.0.4672.2.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 5.3.ah_x_abw_dd_aff $2$ (not in LMFDB) 5.3.af_l_am_j_aj $2$ (not in LMFDB) 5.3.ab_ab_a_j_aj $2$ (not in LMFDB) 5.3.b_ab_a_j_j $2$ (not in LMFDB) 5.3.f_l_m_j_j $2$ (not in LMFDB) 5.3.h_x_bw_dd_ff $2$ (not in LMFDB) 5.3.l_ch_hw_tt_bml $2$ (not in LMFDB) 5.3.ai_bj_aee_kb_atk $3$ (not in LMFDB) 5.3.af_l_am_j_aj $3$ (not in LMFDB) 5.3.af_u_acf_ff_ajs $3$ (not in LMFDB) 5.3.ac_f_ag_j_a $3$ (not in LMFDB) 5.3.ac_o_ay_dd_aee $3$ (not in LMFDB) 5.3.b_ab_a_j_j $3$ (not in LMFDB) 5.3.b_i_j_bb_bk $3$ (not in LMFDB) 5.3.e_l_y_bt_cu $3$ (not in LMFDB) 5.3.h_x_bw_dd_ff $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 5.3.ah_x_abw_dd_aff $2$ (not in LMFDB) 5.3.af_l_am_j_aj $2$ (not in LMFDB) 5.3.ab_ab_a_j_aj $2$ (not in LMFDB) 5.3.b_ab_a_j_j $2$ (not in LMFDB) 5.3.f_l_m_j_j $2$ (not in LMFDB) 5.3.h_x_bw_dd_ff $2$ (not in LMFDB) 5.3.l_ch_hw_tt_bml $2$ (not in LMFDB) 5.3.ai_bj_aee_kb_atk $3$ (not in LMFDB) 5.3.af_l_am_j_aj $3$ (not in LMFDB) 5.3.af_u_acf_ff_ajs $3$ (not in LMFDB) 5.3.ac_f_ag_j_a $3$ (not in LMFDB) 5.3.ac_o_ay_dd_aee $3$ (not in LMFDB) 5.3.b_ab_a_j_j $3$ (not in LMFDB) 5.3.b_i_j_bb_bk $3$ (not in LMFDB) 5.3.e_l_y_bt_cu $3$ (not in LMFDB) 5.3.h_x_bw_dd_ff $3$ (not in LMFDB) 5.3.af_r_abq_dp_agp $4$ (not in LMFDB) 5.3.ab_f_ag_v_abb $4$ (not in LMFDB) 5.3.b_f_g_v_bb $4$ (not in LMFDB) 5.3.f_r_bq_dp_gp $4$ (not in LMFDB) 5.3.ae_l_ay_bt_acu $6$ (not in LMFDB) 5.3.ab_i_aj_bb_abk $6$ (not in LMFDB) 5.3.c_f_g_j_a $6$ (not in LMFDB) 5.3.c_o_y_dd_ee $6$ (not in LMFDB) 5.3.f_u_cf_ff_js $6$ (not in LMFDB) 5.3.i_bj_ee_kb_tk $6$ (not in LMFDB) 5.3.ac_f_ap_bb_abt $9$ (not in LMFDB) 5.3.ac_f_d_aj_bt $9$ (not in LMFDB) 5.3.af_i_d_abh_cu $12$ (not in LMFDB) 5.3.ac_c_a_ap_bk $12$ (not in LMFDB) 5.3.ac_l_as_cf_acu $12$ (not in LMFDB) 5.3.ab_ae_d_d_a $12$ (not in LMFDB) 5.3.b_ae_ad_d_a $12$ (not in LMFDB) 5.3.c_c_a_ap_abk $12$ (not in LMFDB) 5.3.c_l_s_cf_cu $12$ (not in LMFDB) 5.3.f_i_ad_abh_acu $12$ (not in LMFDB) 5.3.c_f_ad_aj_abt $18$ (not in LMFDB) 5.3.c_f_p_bb_bt $18$ (not in LMFDB) 5.3.af_o_abb_bz_adm $24$ (not in LMFDB) 5.3.ac_i_am_bh_abk $24$ (not in LMFDB) 5.3.ab_c_ad_p_as $24$ (not in LMFDB) 5.3.b_c_d_p_s $24$ (not in LMFDB) 5.3.c_i_m_bh_bk $24$ (not in LMFDB) 5.3.f_o_bb_bz_dm $24$ (not in LMFDB)


text:
# Area of oval

• Aug 17th 2008, 07:43 AM
jbuddenh
Area of oval
The following 4th degree polynomial in two variables encloses an oval shape in the x-y plane:

${x}^{4}+{y}^{4}=-2\, \left( y+1 \right) \left( y-2 \right) {x}^{2}+{y}^{2} \left( 2\,y+3 \right)
$

Find the area of the oval.

(Note: just thought this might be a nice problem -- I am not a student and not asking for help).
• Aug 17th 2008, 09:30 AM
Soroban
Hello, jbuddenh!

I have a start on this problem ... but I'm puzzled.
. . Have I made an error ... several errors?

Quote:

The following 4th degree polynomial in two variables encloses an oval shape in the x-y plane:

$x^4 + y^4 \;=\; -2x^2(y+1)(y-2) + y^2(2y+3)$ . Find the area of the oval.

We have: . $x^4 + y^4 \;=\;-2x^2y^2 + 2x^2y + 4x^2 + 2y^3 + 3y^2$

. . . $x^4 + 2x^2y^2 + y^4 \;=\;4x^2 + 3y^2 + 2x^2y + 2y^3$

. . . . . $(x^2+y^2)^2 \;=\;\overbrace{x^2 + 3x^2} +3y^2 + 2x^2y + 2y^3$

. . . . . $(x^2+y^2)^2 \;=\;x^2 + 3(x^2+y^2) + 2y(x^2+y^2)$ . . . Convert to polar coordinates

. . . . . . . . $(r^2)^2 \;=\;(r\cos\theta)^2 + 3r^2 + 2(r\sin\theta)r^2$

. . . . . . . . . . $r^4 \;=\;r^2\cos^2\!\theta + 3r^2 + 2r^3\sin\theta$

Divide by $r^2\!:\;\;r^2 \;=\;\cos^2\!\theta + 3 + 2r\sin\theta$

. . . . . . . . . . $r^2 \;=\;1-\sin^2\!\theta + 3 + 2r\sin\theta \quad\Rightarrow\quad r^2 - 2\sin\theta\!\cdot r + \sin^2\theta - 4 \:=\:0$

. . which factors: . $(r - \sin\theta - 2)(r - \sin\theta + 2) \;=\;0$

. . and we have: . $r \;=\;\sin\theta \pm2$

But this is not an oval . . . We have two limacons.

• Aug 17th 2008, 01:33 PM
shawsend
I'm pretty sure they both have the same loci of points. That is, if $\mathbb{S}=\left\{(r,\theta):r=2+\sin(\theta)\righ t\}$ and $\mathbb{G}=\left\{(r,\theta):r=-2+\sin(\theta)\right\}$, then $\mathbb{S}=\mathbb{G}$. I'm just a little unaccustomed to dealing with negative radii: when the radius is negative, the point in the polar plane is actually located at $(|r|,\theta+\pi)$. So it's just one limicon and can integrate it accordingly.
• Aug 18th 2008, 01:47 PM
jbuddenh
Quote:

Originally Posted by Soroban
Hello, jbuddenh!

I have a start on this problem ... but I'm puzzled.
. . Have I made an error ... several errors?

No errors, good job converting to polar coordinates.

Quote:

Originally Posted by Soroban
[...snip...]

. . which factors: . $(r - \sin\theta - 2)(r - \sin\theta + 2) \;=\;0$

. . and we have: . $r \;=\;\sin\theta \pm2$

But this is not an oval . . . We have two limacons.

I called it an 'oval' because it is a simple closed curve, convex, and with a line of symmetry. I don't think 'oval' has a precise mathematical definition, but that seemed oval to me. Here is a picture of it, created with maple:
http://i36.tinypic.com/iwt0l1.gif
I lied a little because the curve also has an isolated point namely the origin (0,0) which must have dropped out when you divided by r^2. Yes it is a limacon, but as another person pointed out, not two of them. For the area I got $9\pi/2$.
• Aug 18th 2008, 01:52 PM
jbuddenh
Quote:

Originally Posted by shawsend
I'm pretty sure they both have the same loci of points. That is, if $\mathbb{S}=\left\{(r,\theta):r=2+\sin(\theta)\righ t\}$ and $\mathbb{G}=\left\{(r,\theta):r=-2+\sin(\theta)\right\}$, then $\mathbb{S}=\mathbb{G}$. I'm just a little unaccustomed to dealing with negative radii: when the radius is negative, the point in the polar plane is actually located at $(|r|,\theta+\pi)$. So it's just one limicon and can integrate it accordingly.

Yes, I think you are right. Thanks for clarifying the limacon situation. See also the graph of the original x-y equation created with maple, and part of my reply to Soroban in this thread.