The eccentric frame decomposition of central force fields |
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Authors: | Jared M Maruskin Daniel J Scheeres Fred C Adams Anthony M Bloch |
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Institution: | (1) Department of Mathematics, The University of Michigan, Ann Arbor, MI, USA;(2) Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI, USA;(3) Department of Physics, The University of Michigan, Ann Arbor, MI, USA |
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Abstract: | The rosette-shaped motion of a particle in a central force field is known to be classically solvable by quadratures. We present
a new approach of describing and characterizing such motion based on the eccentricity vector of the two body problem. In general,
this vector is not an integral of motion. However, the orbital motion, when viewed from the nonuniformly rotating frame defined
by the orientation of the eccentricity vector, can be solved analytically and will either be a closed periodic circulation
or libration. The motion with respect to inertial space is then given by integrating the argument of periapsis with respect
to time. Finally we will apply the decomposition to a modern central potential, the spherical Hernquist–Newton potential,
which models dark matter halos of galaxies with central black holes. |
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Keywords: | Central force fields Dark matter halos Hernquist– Newton potential Central black hole Axi-symmetric potentials |
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