How to simulate a spherical pendulum in matlab?

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Hi,
I want to simulate a spherical pendulum in matlab. So far, I have found the equation of motion of the spherical pendulum:
But I haven't a clue how to simulate this. Any help whil be useful.
Kind regards, Bas

Accepted Answer

Roger Stafford
Roger Stafford on 11 Feb 2015
Edited: Roger Stafford on 11 Feb 2015
Bas, you have a sign error in the gravity term. It should be:
-g*sin(phi)/L
Use one of matlab's 'ode' solvers to numerically solve these equations. Read about how to use them at:
http://www.mathworks.com/help/matlab/math/ordinary-differential-equations.html
Note that you would have numerical accuracy difficulty if the angle phi approaches near zero because of the division by sin(phi) in the first equation. At that point theta would change very rapidly. That is inherent in the physical situation as measured by the two angles.
  5 Comments
Bas Siebers
Bas Siebers on 22 Apr 2015
Hi Roger,
I started again with solving this problem. Do you known how to transform my coordinates to cartesian coordinates?

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