The solution of Jacobi's virial equation for nonconservative systems and analysis of its dependence on parameters

Details The solution of Jacobi's virial equation for nonconservative systems and analysis of its dependence on parameters The solution of Jacobi's virial equation for nonconservative systems and analysis of its dependence on parameters

Aug 1979

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1979cemec..20..143f&link_type=abstract

Celestial Mechanics, vol. 20, Aug. 1979, p. 143-172.

Physics

8

Jacobi Integral, Nonconservative Forces, Problem Solving, Virial Theorem, Asymptotic Methods, Celestial Mechanics, Form Factors, Moments Of Inertia, Potential Energy

Scientific paper

It is shown that the product of the form factors alpha and beta in expressions for potential energy and the moment of inertia runs to a constant value in the asymptotic time limit of simultaneous collision of all particles for conservative systems. The solution of Jacobi's virial equation for nonconservative systems is obtained. In deriving this result, the property of monotony and continuity of the total energy function for the intervals of the 'smooth' evolution of the system is used. The solution of Jacobi's virial equation for nonconservative and conservative systems near discriminant lines where the moment of inertia is equal to zero is found to possess the same asymptotic behavior as in the case of an arbitrary n-particle system in the asymptotic time limit of simultaneous collision of all n particles. It follows from analysis of the solution of Jacobi's virial equation for nonconservative systems that the amplitude value of oscillations of the moment of inertia decrease to zero near the bifurcation point during the evolution of celestial bodies. Parameters of the bifurcation point and conditions of the system's bifurcation also are found.

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