Equations of movement of partical that slides inside a container


I'm trying to solve the following problem:

"Find the equations of movement of a particle of mass m that slides on the inner surface of a spherical container given by the equation x^2 +y^2 + z^2 = 1, z≤0"

I know I have to use F=ma and I've tried derivating the equation but I don't get anywhere.



Gold Member
The pendulum is a similar problem.
It is a particle moving in a plane and constrained to stay on a circle.
Have a look at how this is usually treated, this might inspire you.
You will see the decomposition of the forces into a component tangential to the trajectory (T) and one perpendicular (N) to it.

You should inform us also on the context of this exercise.
If this is supposed to be an application of the Lagrange method, then i is another story.
No, there is not optimization involved in the problem. I'm familiar with the pendulum but the relation between vectors (with vector calculus notation) and forces is confusing me.
The question about the Lagrange method was really about the Lagrange equation of motion. But from your answer it seems you are not aware of that.

This problem is best solved in spherical coordinates. Are you familiar with them?
Oh, my bad. Yes, but is it necessary? What is the best path to follow?
It = using spherical coordinates. I will try that.

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