- #1

Gbox

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- Homework Statement
- A particle of mass ##m## is moving in a central field with potential ##V(r)## the lagrangian in Spherical coordinate is ##l=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+r^2sin^2\theta\dot{\phi}^2)-V(r)##

- Relevant Equations
- ##P_i=\frac{\partial }{(\partial \dot{p}_i )}##

##H(p,q)=\sum_(i=1)^n(p_i\cdot \dot{r}_i)-L##

##\dot{q}=\frac{\partial H}{(\partial p_i )}##

##\dot{p}_i=\frac{-\partial H}{(\partial q_i }##

3. Find the hamilton equations

4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved.

I got in ##3##:

How can I prove 4?

4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved.

I got in ##3##:

How can I prove 4?