Integrable case of perturbed Keplerian motion

Details Integrable case of perturbed Keplerian motion Integrable case of perturbed Keplerian motion

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988primm..52.1033k&link_type=abstract

Prikladnaia Matematika i Mekhanika (ISSN 0032-8235), vol. 52, Nov.-Dec. 1988, p. 1033-1036. In Russian.

Physics

Celestial Mechanics, Kepler Laws, Orbit Perturbation, Cauchy Problem, Differential Equations, Equations Of Motion

Scientific paper

A general solution to the vector differential equation of perturbed Keplerian motion is obtained for the case where the position and perturbing acceleration vectors are collinear. Variable substitution is used whereby a new independent variable is expressed in terms of the initial values of the phase variables and time is expressed in terms of the elliptic Jacobi function. The two-point boundary value problem for the initial equations is reduced to the Cauchy problem. A parametric expression is obtained for the regularized motion trajectory of a material point under the effect of a central force.

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