Properties of the moment of inertia in the problem of three bodies

Details Properties of the moment of inertia in the problem of three bodies Properties of the moment of inertia in the problem of three bodies

Aug 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..24..345z&link_type=abstract

Celestial Mechanics, vol. 24, Aug. 1981, p. 345-354.

Physics

7

Moments Of Inertia, Three Body Problem, Time Dependence, Angular Momentum, Equations Of Motion, Euler-Lagrange Equation, Inequalities, Jacobi Integral

Scientific paper

Consideration is given to the time dependence of the moment of inertia in the three-body problem. A new statement of Sundman's inequality is obtained in terms of the Lagrange-Jacobi equation, and used, together with the results of Birkhoff (1927), to derive the properties of the moment of inertia for the case of negative energy and nonzero angular momentum, in which the time dependence of the moment of inertia can be represented by a curve with a single minimum which is everywhere concave upwards and rises indefinitely. A new inequality is then derived which may be also used for the case of zero angular momentum, and its implications for the moment of inertia are examined. It is noted that according to the present results and those of Birkhoff, all solutions of the three-body problem near triple collisions are hyperbolic-elliptic for all time.

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