arXiv subjects

J. E. Howard

Publications and source records attributed to J. E. Howard.

2 recordsLinked to original sources

arXiv2009

Straight Line Orbits in Hamiltonian Flows

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 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 generalized Hénon-Heiles potentials having discrete rotational symmetry. SLO's are also found for superpositions of these potentials.

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arXiv2001

Generalizations of the Störmer Problem for Dust Grain Orbits

We consider the generalized Störmer Problem that includes the electromagnetic and gravitational forces on a charged dust grain near a planet. For dust grains a typical charge to mass ratio is such that neither force can be neglected. Including the gravitational force gives rise to stable circular orbits that encircle that plane entirely above/below the equatorial plane. The effects of the different forces are discussed in detail. A modified 3rd Kepler's law is found and analyzed for dust grains.

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