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Toby_phys
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Homework Statement
N point particles of mass mα, α = 1,...,N move in their mutual gravitational field. Write down the Lagrangian for this system. Use Noether’s theorem to derive six constants of motion for the system, none of which is the energy
Homework Equations
Noethers Theorem: If a change ([itex] q_i \implies q_i+\delta q_i [/itex]) creates no change in the Lagrangian the conserved quantity is
[tex] \sum \dot{p_i}\delta q_i [/tex]
The Attempt at a Solution
So my lagrangian is:
[tex]
L=\frac{1}{2}\sum m_i \dot{r}^2_i-\sum_{i\neq j}V(|r_i-r_j|)
[/tex]
With this I can get 2 conserved quantities - momentum (from translational invariance) and angular momentum. How do I get the other 4?