http://arxiv.org/abs/1606.06349
We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an approximate third integral of motion predicting envelopes of the form $Z(R)\propto[\Sigma(R)]^{-1/3}$, where $R$ is the radial galactocentric coordinate, $Z$ is the z-amplitude (vertical amplitude) of the orbit and $\Sigma$ represents the surface mass density of the thin disk. This third integral, which was previously formulated for the case of flattened 3D configurations, is tested for a variety of trajectories in different thin-disk models.
R. Vieira and J. Ramos-Caro
Wed, 22 Jun 16
1/50
Comments: Version accepted for publication at Celestial Mechanics and Dynamical Astronomy. Replaces arxiv version arxiv:1206.6501. The final publication is available at Springer via this http URL