Computer Science
Scientific paper
Mar 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994cosre..31..582r&link_type=abstract
Cosmic Res., Vol. 31, No. 5, p. 582 - 585
Computer Science
Celestial Mechanics: Perturbation Theory
Scientific paper
One of the most convenient algorithms of perturbation theory for conservative mechanical systems in the problems of spaceflight dynamics, celestial mechanics, and solid body dynamics is that of the Hori method. Specifically, it has found application in the problem of celestial body rotation about a mass center. The algorithm of this method provides for the construction of a canonical transformation along the trajectories of the conservative system, the Hamiltonian of which is in the general case a formal series in integral powers of a small parameter, the coefficients of which are determined from a first-order partial differential equation. The explicit direct and reverse variable replacement formulas make it possible to effectively study the behavior of the perturbed system Hamiltonian - specifically to construct the approximate solutions in analytic form on a computer. From among all the solutions of the partial differential equation, the authors select the solution that is 2π-periodic with respect to the angular variable. Thanks to this, the approximate solutions differ very little from the exact solutions on long time intervals. However, the transformations are constructed differently upon approach to the different resonance curves, and with the presence of a double resonance the method loses its effectiveness. In these cases the authors often use for study of the perturbed dynamic system the Poincare method of mapping onto a section, which can be realized numerically on the computer. They shall show how the Hori algorithm can be modified for construction of the mapping in analytic form. The transformation will be defined uniquely for the resonant and nonresonant regions by a formal series in powers of a small parameter with analytic coefficients.
Demin M. V.
Pankratov A. A.
Rodnikov A. V.
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