Straight line orbits in Hamiltonian flows
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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 a family of potentials having discrete rotational symmetry as well as superpositions of these potentials.
KeywordsNatural flows Hamiltonian flows Hénon–Heiles Homogeneous potentials Direct and indirect methods
- Bozis G., Kotoulas T.A.: Three-dimensional potentials producing families of straight lines (FSL). Rendiconti Seminario Facout Scienze Universat Cagliari 74(1–2), 83–98 (2004)Google Scholar
- Szebehely V.: Theory of orbits: the restricted problem of three bodies. Academic Press, New York (1967)Google Scholar
- Szebehely, V.: On the determination of the potential. In Zagar, F., Proverbio, E. (eds.) Il Problema Della Rotazione Terrestre. Bologna, Universit Di Cagliari, 1974. Rendiconti Del Seminario Della Facoltà Di Scienze dell’Università Di CagliariGoogle Scholar