- #1

anubis01

- 149

- 1

## Homework Statement

Find Hamiltons canonical equations for a satellite of mass m moving about a star of mass M at the origin. Consider motion in a plane, using polar coordinates r,[tex]\theta[/tex].

Repeat the process using cartesian coordinates x,y from the start.

## Homework Equations

H=T+V

## The Attempt at a Solution

I did both questions but I'm not exactly sure if I defined the kinetic and potential energies correctly for each case. For polar coordinates I found T=m/2 * (r[tex]\dot{}[/tex]

^{2}+r

^{2}[tex]\theta[/tex][tex]\dot{}[/tex]

^{2}) and potential energy V=V(r)

For cartessian coordinates I found the Kinetic T=m/2(x[tex]\dot{}[/tex]

^{2})

and potential energy V=[tex]\frac{-GMm}{\sqrt{x^2+y^2}}[/tex].

So if anyone can confirm if I set up the kinetic and potential energy equations correctly that would be great.

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