Generalized Lagrangian orbital elements for central force problems

Details Generalized Lagrangian orbital elements for central force problems Generalized Lagrangian orbital elements for central force problems

May 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36...71w&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, May 1985, p. 71-82.

Computer Science

Equations Of Motion, Gravitational Fields, Orbit Perturbation, Orbital Elements, Celestial Mechanics, Double Cusps, Kepler Laws, Laplace Equation, Perturbation Theory

Scientific paper

The definitions and resulting equations of motion are considered for the Lagrangian orbital elements associated with conventional osculating orbit theory for central forces. The analysis indicates that the definitions themselves lead to difficulties which are most apparent in the circular limit. An alternate set of defining relations is presented which eliminates the problems associated with osculating elements. The remaining equation of motion based on these new definitions is reduced to quadratures. This solution completely expresses the orbits for central force problems with no restriction on the eccentricity. Both bounded and open orbits are considered. A generalized Laplace-Runge-Lenz vector is developed and a number of example solutions are presented.

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