Astronomy and Astrophysics – Astronomy
Scientific paper
May 1983
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983cemec..30...31m&link_type=abstract
Celestial Mechanics (ISSN 0008-8714), vol. 30, May 1983, p. 31-47. Research sponsored by the Science and Engineering Research Co
Astronomy and Astrophysics
Astronomy
5
Astrodynamics, Degrees Of Freedom, Hamiltonian Functions, Orbit Perturbation, Satellite Orbits, Algorithms, Circular Orbits, Earth Orbits, Orbit Calculation
Scientific paper
An analytical theory is presented for determining the motion described by a Hamiltonian of two degrees of freedom. Hamiltonians of this type are representative of the problem of an artificial earth satellite in a near-circular orbit or a near-equatorial orbit and in resonance with a longitudinal dependent part of the geopotential. Using the classical Bohlin-von Zeipel procedure the variation of the elements is developed through a generating function expressed as a trigonometrical series. The coefficients of this series, determined in ascending powers of an auxiliary parameter, are the solutions of paired sets of ordinary differential equations and involve elliptic functions and quadrature. The first order solution accounts for the full variation of the resonance terms with the second coordinate.
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