Question

A particle of mass m is constrained to move on

the boundary of an ellipse x^2 + y^2 = 2. Identify

the generalize.d coordinates of this system.

Answer 1

The generalized coordinate is polar angle $\theta$:

$$x=\sqrt{2}\cos\theta\\ y=\sqrt{2}\sin\theta$$

Then

$$x^2+y^2=2(\cos^2\theta+\sin^2\theta)=2$$