Straight Line Orbits in Hamiltonian Flows

Details Straight Line Orbits in Hamiltonian Flows Straight Line Orbits in Hamiltonian Flows

2009-03-28

arxiv.org/abs/0903.4995v1

Celest. Mech and Dyn. Astron. 104:337-352 (2009)

Nonlinear Sciences

Chaotic Dynamics

laTeX with 6 figures

Scientific paper

10.1007/s10569-009-9231-4

We investigate periodic straight-line orbits (SLO) in Hamiltonian force fields using both direct and inverse methods. A general theorem is proven for natural Hamiltonians quadratic in the momenta in arbitrary dimension and specialized to two and three dimension. Next we specialize to homogeneous potentials and their superpositions, including the familiar H\'enon-Heiles problem. It is shown that SLO's can exist for arbitrary finite superpositions of $N$-forms. The results are applied to a family of generalized H\'enon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.

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