Harmonically excited orbital variations
Abstract
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. 5 refs.
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab., CA (USA)
 OSTI Identifier:
 5265474
 Report Number(s):
 UCRL93154; CONF85101461
ON: DE85017102
 DOE Contract Number:
 W7405ENG48
 Resource Type:
 Conference
 Resource Relation:
 Conference: International astronautical federation congress, Stockholm, Sweden, 7 Oct 1985
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASTROPHYSICS; MECHANICS; COMETS; EQUATIONS OF MOTION; ANGULAR MOMENTUM; LAGRANGIAN FUNCTION; ORBITS; DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; PARTIAL DIFFERENTIAL EQUATIONS; 640107*  Astrophysics & Cosmology Planetary Phenomena
Citation Formats
Morgan, T. Harmonically excited orbital variations. United States: N. p., 1985.
Web.
Morgan, T. Harmonically excited orbital variations. United States.
Morgan, T. 1985.
"Harmonically excited orbital variations". United States.
doi:. https://www.osti.gov/servlets/purl/5265474.
@article{osti_5265474,
title = {Harmonically excited orbital variations},
author = {Morgan, T.},
abstractNote = {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. 5 refs.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 1985,
month = 8
}

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