Qualitative analysis of the phase flow of a Manev system in a rotating reference frame

Abstract

The rotating two-body Manev problem is defined by means of the Hamiltonian function with (α, β)∈ℝ⁺×ℝ being two structural parameters. Using the Liouville–Arnold theorem and a particular analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. This analysis, in some aspects very computational, is made with the help of a standard commercial mathematical package.

Keywords:

• Manev rotating system
• Liouville–Arnold theorem
• amended potential
• Hill regions
• momentum map

2000 AMS Subject Classifications :

• 34J15
• 53D17
• 70F07
• 70K42
• 70H14

Acknowledgements

This work has been partially supported by MCYT (grant numbers MTM2005-03860 and MTM2005-06098-C02-01), Fundación Séneca (grant numbers 00684–FI–04 and 05783–PI–07) and JCCM (grant numbers PAI06-0114 and PBC05-011-3).

Notes

The amended potential is also known as effective potential. Its definition can be found in 1 or in 4 where it was originally stated.