Are we always able to express it in a smooth (continuous) curve?

Starboy

I suppose that the time derivative of the generalized coordinates would change as time changes, so could we use a matrix to store the derivatives at each time point?

air-wreck

Are there places where the generalized velocity is fixed and the generalized coordinates are instead computed from the velocities?

Kaxano

Would we ever want to consider generalized coordinates which are not differentiable at certain points?

Are we always able to express it in a smooth (continuous) curve?

I suppose that the time derivative of the generalized coordinates would change as time changes, so could we use a matrix to store the derivatives at each time point?

Are there places where the generalized velocity is fixed and the generalized coordinates are instead computed from the velocities?

Would we ever want to consider generalized coordinates which are not differentiable at certain points?