Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

Details Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies Periodic solutions about the collinear Lagrangian solution in the general problem of three bodies

May 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..24...63b&link_type=abstract

Celestial Mechanics, vol. 24, May 1981, p. 63-82. Research supported by the University of Texas;

Physics

7

Circular Orbits, Equations Of Motion, Orbital Mechanics, Periodic Functions, Three Body Problem, Collinearity, Numerical Integration, Variational Principles

Scientific paper

The article describes the solutions near Lagrange's circular collinear configuration in the planar problem of three bodies with three finite masses. The article begins with a detailed review of the properties of Lagrange's collinear solution. Lagrange's quintic equation is derived and several expressions are given for the angular velocity of the rotating frame. The equations of motion are then linearized near the circular collinear solution, and the characteristic equation is also derived in detail. The different types of roots and their corresponding solutions are discussed. The special case of two equal outer masses receives special attention, as well as the special case of two small outer masses. Finally, the fundamental family of periodic solutions is extended by numerical integration all the way up to and past a binary collision orbit. The stability and the bifurcations of this family are briefly enumerated.

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