Abstract
The problem of Keplerian motion in the uniformly rotating reference frame has been solved in terms of the Kustaanheimo-Stiefel (KS) variables using canonical formalism. No recourse to the Cartesian variables or orbital elements has been required. The form of solution is well suited for the application as a part of symplectic integrator. The results show that the motion is actually the composition of four independent harmonic oscillations and of the rotation in two specific coordinate planes and their conjugate momenta planes. As an example of application, we use the KS symplectic integrator to study the motion of comet C/1997 J2 (Meunier-Dupuoy) under the action of Galactic tides. The comet is found to follow an orbit in commensurability with the Sun motion around the Galactic centre, but the perturbations are not qualified as a resonance.
Highlights
Kustaanheimo-Stiefel (KS) transformation, transforms the three-dimensional Kepler problem into a four-dimensional isotropic harmonic oscillator
A reference frame with the origin in the primary body and uniformly rotating around one of its axes is a common feature of various classical problems in celestial mechanics
Providing an explicit solution to the problem of Keplerian motion in rotating frame in terms of the KuustanheimoStiefel variables was the main objective of the presented work
Summary
Kustaanheimo-Stiefel (KS) transformation, transforms the three-dimensional Kepler problem into a four-dimensional isotropic harmonic oscillator. A reference frame with the origin in the primary body and uniformly rotating around one of its axes is a common feature of various classical problems in celestial mechanics Most often it helps to remove explicit time dependence from potential. In this particular problem, Breiter et al (2007) worked out a symplectic integrator in KS variables using a partition of Hamiltonian into Keplerian part and perturbation. Breiter et al (2007) worked out a symplectic integrator in KS variables using a partition of Hamiltonian into Keplerian part and perturbation The former part requires the knowledge of explicit solution to construct a propagator of coordinates, momenta, and optionally of their variations. The momentum vector R is the velocity vector measured in the fixed frame, whose components are resolved along instantaneous axes of the rotating frame at given epoch
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