Harmonically excited orbital variations

Details Harmonically excited orbital variations Harmonically excited orbital variations

Aug 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985stin...8616242m&link_type=abstract

Presented at the International Astronautical Federation Congress, Stockholm, Sweden, 7 Oct. 1985

Astronomy and Astrophysics

Astrophysics

Equations Of Motion, Euler-Lagrange Equation, Orbital Mechanics, Transfer Orbits, Angular Momentum, Artificial Satellites, Astrophysics, Comets, Harmonic Excitation, Orbits, Spacecraft Orbits, Variations

Scientific paper

Rephrasing the equations of motion for orbital maneuvers in terms of Lagrangian generalized coordinates instead of Newtonian rectangular Cartesian coordinates can make certain harmonic terms in the orbital angular momentum vector more readily apparent. In this formulation the equations of motion adopt the form of a damped harmonic oscillator when torques are applied to the orbit in a variationally prescribed manner. The frequencies of the oscillator equation are in some ways unexpected but can nonetheless be exploited through resonant forcing functions to achieve large secular variations in the orbital elements. Two cases are discussed using a circular orbit as the control case: (1) large changes in orbital inclination achieved by harmonic excitation rather than one impulsive velocity change, and (2) periodic and secular changes to the longitude of the ascending node using both stable and unstable excitation strategies. The implications of these equations are also discussed for both artificial satellites and natural satellites. For the former, two utilitarian orbits are suggested, each exploiting a form of harmonic excitation.

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