The extended phase space formulation of the Vinti problem

Details The extended phase space formulation of the Vinti problem The extended phase space formulation of the Vinti problem

Dec 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977cemec..16..441a&link_type=abstract

Celestial Mechanics, vol. 16, Dec. 1977, p. 441-458.

Mathematics

1

Artificial Satellites, Oblate Spheroids, Orbital Mechanics, Phase-Space Integral, Satellite Orbits, Vinti Theory, Canonical Forms, Hamilton-Jacobi Equation, Hamiltonian Functions, Harmonic Oscillators, Orbit Calculation, Orbital Elements, Run Time (Computers), Satellite Perturbation, Transformations (Mathematics)

Scientific paper

Vinti's theory of motion about an oblate spheroid is extended by the phase space method with a new independent variable similar to the true anomaly. This decouples the radius and latitude equations into two perturbed harmonic oscillators which are solved up to terms in the J(4,2) harmonic by Lindstedt's method. These solutions are then used to solve the other integrals in the Hamilton-Jacobi equations. This yields a new set of canonical variables similar to the Delaunay similar variables. The new Hamiltonian which is a function of the new momenta only is then developed to terms of the order of J(4,2). The final solutions are expressed as a function of a set of nonsingular variables that are well defined for small eccentricity and low inclination.

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