Straight line orbits in Hamiltonian flows

@article{Howard2009StraightLO,
  title={Straight line orbits in Hamiltonian flows},
  author={James E. Howard and James D. Meiss},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={2009},
  volume={105},
  pages={337-352}
}
  • J. HowardJ. Meiss
  • Published 28 March 2009
  • Physics, Mathematics
  • Celestial Mechanics and Dynamical Astronomy
We investigate 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 for arbitrary dimensions and is considered in more detail for two and three dimensions. Next we specialize to homogeneous potentials and their superpositions, including the familiar Hénon–Heiles problem. It is shown that SLO’s can exist for arbitrary finite superpositions of N-forms. The results are applied to… 
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