| Affiliation: | 1.Instituto de Astronomia, Geofísica e Ciências Atmosféricas,Universidade de S?o Paulo,S?o Paulo,Brazil;2.Departamento de Física,Universidade Federal de S?o Carlos,S?o Carlos,Brazil |
| Abstract: | 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 [varSigma (R)]^{-1/3}), where R is the radial galactocentric coordinate, Z is the z-amplitude (vertical amplitude) of the orbit and (varSigma ) 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. |
