Conserved quantities + galactic dynamics

[rjl2007]

Hi,

I've been attempting to use pysr to find conserved quantities along galaxy orbits in 6D phase space.
For the tests I've run so far I'm using a spherical gravitational potential (eg a Plummer model) for which there should be 4 conserved quantities - energy + the 3 components of angular momentum. I'm not attempting to find energy at the moment (sqrt is left out as a unary operator) but I was hoping to find the angular momentum components. In general, I find one component but not all three. The data file I supply contains position + velocities for 2 orbits with a function value set to 1 for the first orbit and 2 for the second (as in the AI Poincare paper). The question I have is how can I find the other components of angular momentum ? Are you able to provide any advice / guidance please ?

Richard Long