Spherical Pendulum with Animation - Maple Application Center
Application Center Applications Spherical Pendulum with Animation

## Spherical Pendulum with Animation

Author
: Dr. Ahmed Baroudy
This Application runs in Maple. Don't have Maple? No problem!

Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.
Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.
The idea is:
1- to get the differential equations of motion for the Spherical Pendulum (SP),
2- to solve them,
3- to use  Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,
4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,
5- finally to work out the necessary steps for the purpose of animation.
It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:
" the length of the output exceeds 1 million".
Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction.
Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.

It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.
This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations & programming as I did.

#### Application Details

Publish Date: March 26, 2012
Created In: Maple 14
Language: English

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#### Tags

mechanics calculus differential-equation