The solution of Jacobi's virial equation for nonconservative systems and analysis of its dependence on parameters |
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| Authors: | V I Ferronsky S A Denisk S V Ferronsky |
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| Institution: | (1) Water Problems Institute of the Academy of Sciences of the U.S.S.R., 13/3, Sadovaya-Chernogriazskaya, 103064 Moscow, U.S.S.R. |
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| Abstract: | It is shown that the product of the form-factors  and  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 nonconservative systems.The solution of Jacobi's virial equation for nonconservative systems is obtained. In deriving this result, we used the property of monotony and continuity of the total energy function for the intervals of the  smooth evolution of the system.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 behaviour as in the case of an arbitraryn particles system in the asymptotic time limit of simultaneous collision of alln 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 bifurcational point during the evolution of celestial bodies. Parameters of the bifurcational point and conditions of the system's birfurcation also are found.
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