# Finding conserved quantities from Hamiltonian when Symmetry is not evident [closed]

A particle is moving in 3D space, under a potential

$$V = -\frac{\alpha}{r}-\frac{\vec{r} \cdot \vec{\mu}}{r^3 }$$

where $\vec{\mu}$ is some constant vector. I need to show there are three conserved quantities. By writing the Lagrangian or Hamiltonian in spherical co-ordinates, it is evident that energy and angular momentum are conserved. But where is the third conserved quantity? Any guidance would be appreciated.

## closed as off-topic by Colin McFaul, Brandon Enright, JamalS, John Rennie, DanuNov 24 '14 at 8:30

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