The formal integrals of the restricted planar problem of the three bodies

Details The formal integrals of the restricted planar problem of the three bodies The formal integrals of the restricted planar problem of the three bodies

Jun 1985

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985cemec..36..105t&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 36, June 1985, p. 105-121.

Physics

Circular Orbits, Equations Of Motion, Hamilton-Jacobi Equation, Integral Equations, Power Series, Three Body Problem, Celestial Mechanics, Collisions, Orbital Mechanics, Polynomials, Trigonometric Functions

Scientific paper

The first integrals of motion of the restricted planar circular problem of three bodies are constructed as the formal power series in r1/2, r being the distance of a moving particle from the primary. It is shown that the coefficients of these series are trigonometric polynomials of an angular variable. Some particular solutions have been found in a closed form. The proposed method for constructing the formal integrals can be generalized to a spatial problem of three bodies.

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