The extended phase space formulation of the Vinti problem
Abstract
The Vinti problem, motion about an oblate spheroid, is formulated using the extended phase space method. The new independent variable, similar to the true anomaly, decouples the radius and latitude equations into two perturbed harmonic oscillators whose solutions to the order of the fourth power of J2 are obtained using Lindstedt's method. From these solutions and the solution to the HamiltonJacobi equation suitable angle variables, their canonical conjugates and the new Hamiltonian are obtained. The new Hamiltonian accurate to the order of the fourth power of J2 is a function of only the momenta.
 Publication:

AIAA and AAS, Astrodynamics Conference
 Pub Date:
 August 1976
 Bibcode:
 1976aaas.confQ....A
 Keywords:

 Equations Of Motion;
 HamiltonJacobi Equation;
 Orbit Perturbation;
 Satellite Orbits;
 Vinti Theory;
 Canonical Forms;
 Error Analysis;
 Harmonic Oscillators;
 Oblate Spheroids;
 Orbital Mechanics;
 Astrodynamics