Hello,
I want to analyze the dynamic equation of motion for a body going on a sphere surface. However, everything I found is the dynamic equation of motion for a body on a 2D plane, not on a 3d space, such as a sphere surface.
What would I do?
Thanks.
You could use Lagrangian Mechanics (https://en.wikipedia.org/wiki/Lagrangian_mechanics)
Write the spherical motion as
x=r*cos(phi) * sin(theta)
y=r*sin(phi) *sin(theta)
z=r*cos(phi)
where r is a constant and phi and theta are your generalized coordinates.
Then define your Lagrangian and derive the equations of motion.
Including rigid body orientation complicates matters a bit but the same approach can be used.
See if the following suggestion helps you. The suggestion is to start with a simple example, e.g. the spherical pendulum (see https://www.ma.imperial.ac.uk/~pavl/ASHEET2.PDF or other similar).
Any dynamic condition can be extended from 2D to 3D. The spring constant input and mass are needed in 3 directions. Motion of the mass is to be decoupled into individual 3 directions. It is similar to what is being done in 3D FEM, and solutiong using eigen value analysis in 3D.
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