Explorer 1 was the first satellite sent into space by the United States. It was a scientific instrument that led to the discovery of the Van Allen radiation belt. In order to keep its orientation, the satellite was spin stabilized. Unexpectedly, shortly after launch, Explorer 1 flipped the axis of rotation. The animation below shows, on the left, Explorer 1 in its initial state after launch, rotating about the axis of minimum moment of inertia. On the right side, 100 minutes later in the simulation, Explorer 1 rotates about the axis of maximum moment of inertia. This unintended behavior could not be explained immediately. Finally, structural damping in the four whip-like antennas was made responsible for the flip (explained here).

The flip can be reproduced with MapleSim using flexible beam components with damping enabled. Without damping and without slight angular misalignment at launch the flip does not manifest.

The simulation is only of qualitative nature since data of the antennas could not be found. On images of Explorer 1, the antennas look prebend and show large deflections of about 45 degrees under gravity. Since rotation of the satelite stretches the antennas, no modeling of large deflections needed to be considered in the simulation and rather stiff antennas (2 mm in diameter) without spheres at their ends were used. (Modeling large deflections with high fidelity might only be considered if the unfolding process of the antennas at launch is of interest. This should be modeled with several flexible beam components.)  

The graph bellow shows the evolution of the angular velocity in x direction. Conservation of angular momentum reduces the angular velocity when the satellite starts flipping towards a rotation about the axis of maximum moment of inertia.

Not long ago such simulations would have been worth a doctoral thesis. Today its rather straight forward to reproduce the flip with MapleSim.

Not so easy is the calculation of energy and angular momentum (for the purpose of observing how well numerics preserve physical quantities in rather long calculations. After all, the solver does not know the physical context). Such calculations would require access to the inertia matrix of the cylinder component including a coordinate transform into the frame of reference where the vector of rotation can be measured.

In case such calculations are possible with MapleSim, it would be nice if someone can update the model or at least indicate how calculations can be done.

Explorer_1_Parameters_and_links.mw

Explorer_1.msim

On a side note: I learned from the flip in an excellent series of lectures on dynamics. Wherever our professor could, he came up with animation in hardware. In this case, he could only provide an exciting story about the space race and sometimes fruitful mistakes in science. That’s why I still remember it.

Adeptes de Maple Learn, nous avons de bonnes nouvelles pour vous! Nous avons fait une mise à jour de Maple Learn avec quelques fonctionnalités supplémentaires que nous sommes ravis de partager avec vous.

Tout d'abord, nous avons ajouté des fonctionnalités de Conception réactive à Maple Learn. Cela signifie que lorsqu'un écran est plus petit ou rétréci, l'interface de Maple Learn change pour refléter cela. Cela vous permet d'avoir encore plus d'espace disponible, quelle que soit la taille de votre écran ! Par exemple, lorsque votre écran est suffisamment petit, et que vous cliquez dessus sur les palettes, une petite boîte de dialogue contextuelle s’ouvrira en dessous d'elles, au lieu d’avoir tout leur contenu dans la barre d'outils.

Parallèlement à cela, une icône de redimensionnement d'image a été ajoutée à la barre d'outils pour faciliter le redimensionnement des images insérées dans votre document.

Comme note finale sur la conception réactive, plusieurs de nos menus ont été combinés en un seul, désigné par le menu latéral dans le coin supérieur gauche (illustré ci-dessous, à gauche). C'est là que vous trouverez les menus  fichier, édition, exemples et aide. Si vous cherchez le menu des paramètres, vous le trouverez entre le symbole premium et votre photo de profil en haut à droite. Ceci est désigné par trois points empilés les uns sur les autres (illustrés ci-dessous, à droite).

Nous avons également ajouté plus de raccourcis clavier et augmenté la prise en charge du clavier AZERTY. La liste mise à jour est disponible ici. Nous espérons que ces nouveaux raccourcis vous aideront à créer des documents plus facilement.

Parallèlement à la prise en charge du clavier AZERTY, nous avons renforcé la prise en charge de nos utilisateurs francophones. De nombreux autres documents sont désormais disponibles en français et nous avons résolu un problème où les caractères latins étendus ne s'affichaient pas correctement.

Les graphiques cliquables sont là ! Maple Learn inclut désormais une fonctionnalité qui permet aux utilisateurs de colorier nos graphiques cliquables. Ces documents sont créés à l'aide de Maple et permettent de générer des documents de coloriage par numéro ou différentes visualisations pour les théorèmes qui impliquent des graphiques, comme ce document. D'autres documents seront disponibles ultérieurement dans la galerie de documents, située ici.

Dites-nous ce que vous pensez des nouvelles fonctionnalités ci-dessous ! Nous espérons que vous apprécierez les utiliser pour créer de nouveau documents Maple Learn.

Works cited:

Anderson, Jill. “The Benefit of Interactive Learning.” Harvard Graduate School of Education, 2014, https://www.gse.harvard.edu/news/14/11/benefit-interactive-learning.

Kutbiddinova, Rimma, et al. “The Use of Interactive Methods in the Educational Process of the Higher Education Institution.” INTERNATIONAL JOURNAL OF ENVIRONMENTAL & SCIENCE EDUCATION, 2016, Accessed 2022.

Maple Learn enthusiasts, we’ve got some exciting news for you! We’ve updated Maple Learn with a few more features that we’re excited to share with you.

First, we’ve added responsive design features to Maple Learn. This means that when a screen is smaller or shrunk the Maple Learn interface changes to reflect that. This lets you have even more canvas space, regardless of your screen size! For example, when your screen is small enough, the palettes, when clicked on, give a small pop-up dialogue below them, instead of their options also appearing in the toolbar.

Along with that, a resize image icon has been added to the toolbar to make it easier to resize the images you’ve inserted into your document.

As a final note on responsive design, several of our menus have been combined into one, designated by the hamburger icon in the top left corner (Shown below, left). This is where you’ll find the file, edit, examples, and help menus. If you are looking for the settings menu, it can be found between the premium symbol and your profile picture in the top right. This is designated by three dots stacked on top of each other (shown below, right).

We’ve also added more keyboard shortcuts, and increased support for the AZERTY keyboard. The updated list can be found here. We hope these new shortcuts will help you create documents more easily.

Along with the support for the AZERTY keyboard, we’ve increased support for our French language users. Many more documents are now available in French, and we’ve resolved an issue where Latin extended characters weren’t being displayed properly.

Clickable plots are here! Maple Learn now includes functionality which allows users to color our clickable plots. These documents are created through Maple scripting, and allow for colour-by-number documents, or different visualisations for theorems that involve graphics, such as this document. More documents will be available in the document gallery later, located here.

Let us know what you think of the new features below! We hope you enjoy using them in new and exciting ways.

It’s midterm season in North America! I know, I know, you see enough reminders at school. However, we’re here to help with those tough midterms, with tips good for those who are taking their first midterms or who have already taken many.

I surveyed the co-op students working at Maplesoft, and collected some of their best study tips and mindsets surrounding midterms. Maplesoft hires many co-ops, as a piece of their education in work experience.

Let’s start with studying! One thing many of the students brought up was the importance of notetaking. Even if the lectures are recorded, or PowerPoints are given, it’s important to take notes that you can study from, that are more succinct. As well, another discussed the importance of doing many different types of studying, in order to keep you interested and focused. For example, using flashcards and answering practice problems, instead of only using flashcards.

So, how can Maplesoft help with your studying? Let’s start with a video. In this video, Justice explains how first year math can be explored using Maple Learn’s features. He walks through using the document gallery, which we’ll talk about later, along with the power of Maple Learn.

You can also create your own study sheets in Maple Learn, to reference later, or to simply practice what you know! One suggestion would be to create a sheet as though you’re teaching someone else, as teaching can be a great way to learn concepts and cement them in your mind.

These are just some of the many ways that Maple Learn can be used to improve your studying! Play around with introducing Maple Learn into your study routine, and I know you’ll find a method that works for you.

Are you having trouble grasping some advanced concepts? We have many different documents in the document gallery, available here. These documents typically fall under 3 categories: explanation documents explaining theory, example documents showing how to apply the theory, and then practice problems for you to solve that include solutions.

Proofs were a topic the students considered an advanced topic, and as such we’ll use that as an example. A simple search brings up many documents, ranging from the proof of the derivative of sine (here) to the Taylor’s Theorem proof (here). These documents are available for a wide variety of topics, from calculus to graph theory to kinematics.

Time Management is another piece that many of the students identified. We know this can be hard, especially when there are so many things to juggle, so we’ve created a document to help you plan out your time, available here!

Using the document, you can see how many hours in a day that you’re using for sleep, studying, and everything else you can think of. We hope this helps you to keep track of just how many hours in a day you can realistically study!

Now, we know that studying isn’t the only hard part of a midterm. The mindset piece is critical, along with studying. Let’s see what the students had to say about it!

One of the students surveyed responded with “I am going to fail at some point. It is inevitable, and that is okay”. This is a great mindset for everyone to have. Remember that even failure isn’t failure. Learning something from any experience is a success, even if the outcome wasn’t what you wanted. There’s always next time, and time to learn even more and improve.

Another student discussed the importance of a positive mindset, saying “Stay calm, stay confident, and as long as you try your best you will do great!” Remember, in the end, the best you can do is all you can do.

We know midterms are a stressful time. Take care of yourself as we at Maplesoft continue to support you.

Auto paste last entry

So maple uses % as the last expression entry.  My suggestion is to use Crtl+Space on the % command to re-display the last expression.  Yes one could easily use the mouse to select the last entry then Crtl+c and Crtl+v. 

Or maybe the command Crtl+Shift+L to auto paste last entry. 

**edit** actually I would prefer the Crtl+Shift+L option to auto paste the last entry.

** Appears to be a suggestion I made earlier https://www.mapleprimes.com/questions/148867-Is-There-A-Way-To-Recallrepeat-Previous

Vous venez de découvrir vos résultats du bac blanc et n’avez pas obtenus les résultats espérés à l’épreuve de mathématiques ?

Maple Learn pourrait vous aider à améliorer vos connaissances et vous préparer pour le vrai baccalauréat.

Commencez par revoir les théorèmes et définitions essentielles en explorant les documents de la galerie Maple Learn. Si vous avez des doutes sur certaines définitions; n’hésitez pas à utiliser les outils graphiques de Maple Learn pour approfondir vos connaissances

Consultez ces documents ici et ici.

Ensuite entrainez-vous à faire vos exercices avec Maple Learn

Consultez ce document ici.

Et enfin vérifiez vos résultats avec la Calculatrice Maple pour voir les étapes de résolutions :

N’hésitez pas à partager en commentaire vos astuces pour réviser avec Maple Learn ou la Calculatrice Maple!

Happy Valentine’s Day! Love is celebrated all around the world on this day, but did you know of some other love celebrations, and some of the mythology around the holiday?

First of all, Cupid. We all know of the image of Cupid and his bow, shooting arrows to make couples fall in love. But where exactly did this come from?

Cupid is a Latin deity, the son of Venus and Mars. With his parents being love and war, it’s no surprise that he ended up with a bow! In one legend, he shoots a golden arrow at Apollo, which makes him fall in love with a nymph. Unfortunately for Apollo, he also shoots a lead arrow at the nymph, making her repulsed by him.

Roses are another popular tradition with Valentine’s Day. Red roses persist as a symbol of Aphrodite, the mother of Cupid, and are a symbol of love. Did you know you can draw them in Maple Learn with our geometry palette? See one rendition below of a stained glass rose. The link to the document is HERE.

Now, there are a few other love traditions around the world. Did you know that not everyone celebrates love only on Valentine’s Day? There are other important days around the world, and some pre-date Valentine’s Day.

For example, in China, the Miao people celebrate the Sister’s Meal Festival, likely our earliest form of a Valentine’s Day tradition in the world. This occurs in March. Young women make dyed rice representing the different seasons, and when the men come by to sing, they give them packages of the rice. Inside the rice are objects, each with different meanings. A pair of red chopsticks means the woman returns the man’s affection, while one red chopstick is a polite refusal. A clove of garlic or a chili pepper means a strong refusal, and pine needles mean that she is waiting for him to woo her.

We’ve created a document to join in on the fun, even if you’re not participating in this Festival this year. Follow the link HERE to work with fraction tiles to pack your own rice packages, and your own responses to declarations of love. 

We hope everyone has a lovely Valentine’s day!

You heard us right! With the new update of Maple Learn, we’ve added a few more interesting features, perfect to keep your math learning going.

Before we dig too far into these exciting features, we just have one quick thing to let you know about. We have updated the font sizes for Maple Learn text, adding 20 and 22 point font, and removing 36 and 120 point font.

Now, let’s talk new features. First, we’ve added support for partial derivatives, allowing you to calculate derivatives for functions with two or more variables. How does this work? Well, take a look at our example document HERE. The button for entering a partial derivative is located in the functions palette. You can plot them too (shown below)!

We’ve also added support for shaded Geometric Primitives. Remember our earlier post about MAPLE LEARN ART? Well, now you can color in your shapes! This allows for further math-related art, or ease of communication while teaching about area, or really, anything else you can think of! See how to use this HERE. In essence, with the shaded command, you can now place a geometric primitive inside the shaded command, which shades it! As well, you can assign a variable to a geometric primitive, and then place that inside the shaded command. This allows for a different color outline than the shaded section.

Ever wanted to create a sequence in Maple Learn? Well, now you can easily, with our new sequence support. The syntax is simple, focusing on the start, end, and steps. See how to use this HERE. We hope this can be used for all kinds of documents!

We hope you enjoy all the new features we’ve added to Maple Learn. Let us know in the comments what you think of them, and show us what you’re working on! Simply leave a comment with a link to a Maple Learn document, and we’ll gladly take a look at your ideas.

We have just issued a critical fix to Maple, MapleSim, and Maple Flow running on macOS.

We have heard from some users who were experiencing serious problems with doubled characters while using Maplesoft products on macOS, including these reports on MaplePrimes. Further investigation determined that these problems appear specifically on macOS 11 and macOS 12.  I am happy to report that we have now corrected the problem, and a patch is available. 

Anyone who uses macOS 11 or macOS 12 should install this update immediately. We also strongly recommend that all macOS users install this update, to avoid problems that may be triggered by future updates to your operating system.

To obtain this update:

• If you have Maple only, follow the instructions on the Maple 2021.2.1 update page.
• If you have MapleSim, visit the MapleSim 2021.2.1 update page.
• If you have Maple Flow, follow the instructions for Maple Flow 2021.2.1.

For those who have experienced problems, we apologize for the inconvenience and thank you for your patience while we worked to find a solution.

Maple users may notice unexpected results when calculating standard deviations with weights.

This is because the notion of weights used by Maple is not exactly the commonly used notion of repeated measurements.

Maple uses the NAG library from the Numerical Algorithms Group to compute the standard deviation in the presence of weights. The formula that is used is given in their documentation: https://www.nag.com/numeric/cl/nagdoc_cl25/pdf/g01/g01aac.pdf.

Download standard-deviation-weights-help-example.mw

Happy Lunar New Year to everyone here in the MaplePrimes community, as we enter the Year of the Tiger! There are different traditions followed in the many countries around the world where the Lunar New Year is celebrated. In my own Canadian-Chinese family, we usually cook a big meal and share with family members and friends. 

The pandemic has made this year's celebration more muted, but I did cook a large batch of our favourite dumplings and made up several packages to take to friends. That led to the question: how many ways can I arrange 10 dumplings on a plate from the 3 kinds I made? Of course, that called for a Maple Learn document to compute the answer: A Counting Problem: Selecting Dumplings
 

I was also interested in understanding the formula used in this computation, and so I created a second document showing a special case of this problem. By moving the sliders around, you can see how the "Stars and Bars" method for counting the ways one can choose a number of items from distinct bins works: Visualization the Stars and Bars Method.

I hope you enjoy trying out these documents and I wish everyone good health, happiness and prosperity in the coming year!

In November, I posted a message announcing that we have been working on an updated version of the Application Center, and invited comments from anyone wanting to check out the beta site. I received multiple comments, both as comments to that post, as well as directly, and we made a lot of changes based on the feedback. Thank you very much to everyone who responded.

I am now very happy to report that the new Application Center is now open to the public!

For those who aren't familiar with it, the Application Center has been around for over 20 years, and it provides a place for our user community to post and share their work. It includes over over 2,700 applications and examples covering a wide array of topics and disciplines, and all are freely available to download.

The previous version of the Application Center was overdue for a refresh. And while we were in there applying a fresh coat of paint, we also took the opportunity to add some new features and capabilities that we hope you will enjoy. As a quick summary of what has changed:

• The look and feel has been significantly updated. It is cleaner, more modern and easier to use.
• In addition to search, user-created collections and tags make it easier than ever to find and discover content.
• Logged-in users can customize the site by pinning their favorite collections and content.
• Logged-in users can also take advantage of their community reputation to help maintain the content in MaplePrimes, and your contributions will now contribute to your reputation scores. For example, when someone likes one of your apps, your reputation score will be increased by 5.
• In addition to Maple content, Maple Flow documents are also now included. The collection is very small right now, but it will grow quickly.

There are plenty of other features and enhancements as well.

So without further ado, I invite you to check out the Application Center and to continue to provide your comments and suggestions!

Bryon

When I was in middle school, I was really into puzzles.  At one point I attempted the Three Utilities Problem.  This famous problem is deceptively simple: three houses and three “utilities” (heating, water, and electricity) are represented by dots on a flat piece of paper.  The goal is to connect each house to the three utilities without crossing any lines.

Figure 1: A starting setup.

I spent hours drawing lines.  I eventually looked it up online, and the internet told me that the problem was impossible.  I didn’t believe it, and tried for several more hours until I was forced to accept its impossibility.  I still remember this intense stint of puzzling to this day.

Figure 2: Cue twelve-year-old me saying “I’ll get it eventually…”

Looking back, I wonder if this sparked my interest in graph theory.  I know now that the Three Utilities Problem is truly unsolvable.  I know that the graph’s formal name is K_3,3 and I know a full graph theory proof explaining its nonplanarity.  Nevertheless, I still love this puzzle, and I’ve recently recreated it in Maple Learn.

To do this, I created a table of x and y values and plotted all of them using the Point() command.  This allows the points to be fully click-and-drag-able.  Line segments joining two points automatically move with the points as well.  We then have a fully interactive graph directly in the Maple Learn plot window.  I can move the “houses” and “utilities” around all I want to try and solve the unsolvable.  I can also create other graphs to further explore planarity, paths, matchings, or any other aspects of the wide world of graph theory.

If you want to check out the document for yourself, it can be found here. 

A user wondered how to have Maple produce a desired form of a solution

Download question-better-spacing.mw

We suggested the closest they might be able to get is using simplify like so:

Download suggestion.mw