(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A body of mass M moves (in a gravitational field g) on the inner surface of given by equation:

[tex]z=\frac{1}{2a}(x^{2}+y^{2})[/tex]

(a is positive)

Reduce the question of finding the motion to quadratures.

2. Relevant equations

3. The attempt at a solution

I used Lagrange equations (1st kind) to find relevant equations for x, y and z, and after separating variables, transformation to polar coordinates [tex](r, \phi, z)[/tex] etc. I came up with the following equation (C is a constant dependent on initial conditions):

[tex]\ddot{r}-\frac{C}{r^{3}}=-\frac{1}{a^{2}}(r{\dot{r}}^{2}+r^{2}\ddot{r})-\frac{g}{a}r[/tex]

I don't have any idea how to integrate this equation, but maybe I've done things in an unnecessarily complicated way...

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# Homework Help: Motion on a paraboloid

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