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.



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