Application of Hamilton's law of varying action to the restricted three-body problem

Details Application of Hamilton's law of varying action to the restricted three-body problem Application of Hamilton's law of varying action to the restricted three-body problem

Oct 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980cemec..22..255h&link_type=abstract

Celestial Mechanics, vol. 22, Oct. 1980, p. 255-266.

Mathematics

Dynamical Systems

7

Approximation, Orbital Mechanics, Three Body Problem, Power Series

Scientific paper

The 'Law of Varying Action', originally published by Hamilton in 1834, was recently employed by Bailey in devising a technique for generating power series characterizing the motions of dynamical systems. Furthermore, Bailey's method permits one to construct these series in a simple and direct way, without using the associated differential equations of motion. In the present paper, Hamilton's law is developed in its most general form and is used to produce series solutions of the restricted three-body problem. Finally, for illustrative purposes, numerical results are presented for several symmetric periodic orbits.

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