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Physics Courseware Support: Mechanics
Hi
The attached worksheet is the final version that appears in Maple 2023 as Courseware support for Mechanics in the context of Physics courses. Everything below also works in Maple 2022.2 with the last Maplesoft Physics Updates for that release..
What follows is presented as "Topic > Problem > Solution", with typical symbolic problems and how you can solve them on a worksheet. As such, this material does not intend to compete with textbooks nor with teacher's notes but to be a helpful complement, as in "what can computer algebra really do to support the learning activity". Mainly, allow for focusing the logic and thinking while the computer takes care of the intricacies of the algebraic manipulations, that when computing with paper and pencil so frequently take mostly all of our focus.
The material, thus, has 70 solved problems covering all the sort-of-syllabus of hyperlinks below. The presentation uses notation as in textbooks and illustrates different techniques, several not present in help pages. It also shows why it is relevant to have a Vectors package that handles abstract vectors as well as projections using unit vectors, not matrix representations for them. Your feedback about everything you see in the worksheet - suggestions for new topics or problems, or anything else - can be useful and is welcome.
Due to the length of this material (~100 pages), out of the 70 problems, below I left open (visible) the Solution sections of only a few of them, illustrating different things, also new functionality e.g. the first and last ones. That is sufficient to have an idea of what this is about. At the end there is a Maple worksheet with the same contents and a PDF file of the same with all the sections open.
With the best wishes for 2023.
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Explore. While learning, having success is a secondary goal: using your curiosity as a compass is what matters. Things can be done in many different ways, take full permission to make mistakes. Computer algebra can transform the algebraic computation part of physics into interesting discoveries and fun.
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The following material assumes knowledge of how to use Maple. If you feel that is not your case, for a compact introduction on reproducing in Maple the computations you do with paper and pencil, see sections 1 to 5 of the Mini-Course: Computer Algebra for Physicists . Also, the presentation assumes an understanding of the subjects and the style is not that of a textbook. Instead, it focuses on conveniently using computer algebra to support the practice and learning process. The selection of topics follows references [1] and [2] at the end. Maple 2023.0 includes Part I. Part II is forthcoming.
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Part I
| 1. |
Position, velocity and acceleration in Cartesian, cylindrical and spherical coordinates
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| a. |
The position  as a function of time
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| b. |
The velocity 
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| c. |
The acceleration 
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| d. |
Deriving these formulas
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| e. |
Velocity and acceleration in the case of 2-dimensional motion on the x, y plane
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| 1. |
The equations of motion
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| i. |
The equations of motion - vectorial form
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| ii. |
The case of constant acceleration
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| iii. |
Motion under gravitational force close to the Earth's surface
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| iv. |
Motion under gravitational force not close to the Earth's surface
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| i. |
Different acceleration in different regions
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| ii. |
The equations of motion using tensor notation
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| B. |
Curvilinear coordinates
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| ii. |
The equations of motion
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| iii. |
Static: reactions of planes and tensions on cables
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| b. |
Conservation of the total energy of a closed system or a system in a constant external field
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| c. |
Conservation of the total momentum of a closed system
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| d. |
Conservation of angular momentum
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