Jacobi Dynamics -

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Biographie:
V.I.Ferronsky obtained his Ph.D. and Dr. Sci. in Nuclear Geophysics. He is Professor of Engineering Geology and Hydrogeology. His positions are: Assistant Professor of Dept. of Soil Mechanics in Civil Engineering Institute, Moscow (1952 -1957)...

Sommaire:
1. Introduction.- Principle of mutual reversibility.- Action and integral canonical pairs.- Integral characteristics in the study of dynamics of natural systems.- Method of moments: specific features in the integral approach and first moments.- 2. Universality of Jacobi's Virial Equation for Description of Dynamics of Natural Systems in Terms of Integral Characteristics.- Derivation of Jacobi's virial equation from Newtonian equations of motion.- Derivation of generalized Jacobi's virial equation for dissipative systems.- Derivation of Jacobi's virial equation from Eulerian equations.- Derivation of Jacobi's virial equation from Hamiltonian equations.- General covariant form of Jacobi's virial equation.- Relativistic analogue of Jacobi's virial equation.- Derivation of Jacobi's virial equation in quantum mechanics.- 3. Solution of Jacobi's Virial Equation for Conservative Systems.- Solution of Jacobi's virial equation in classical mechanics.- Solution of Jacobi's virial equation in hydrodynamics.- Equivalence of the Schwarzschild solution and solution of Jacobi's virial equation (static description).- The hydrogen atom as quantum mechanical analogue of the two-body problem.- 4. Perturbed Virial Oscillations of a System.- Analytical solution of generalized equation of virial oscillations.- Solution of Jacobi's virial equation for a dissipative system.- Solution of Jacobi's virial equation for a system with friction.- 5. Relationship Between Jacobi Function and Potential Energy.- Asymptotic limit of simultaneous collision of mass points for a conservative system.- Asymptotic limit of simultaneous collision of mass points for non-conservative systems.- Asymptotic limit of simultaneous collision of charged particles of a system.- Relationshipbetween Jacobi function and potential energy for a system with high symmetry..- 6. Applications in Celestial Mechanics and Stellar Dynamics.- Solution of Jacobi's virial equation for Trapezium Orion type systems.- Damping virial oscillations.- Application to the problem of the Moon's motion.- Lyapunov stability of motion.- 7. Applications in Astrophysics, Cosmogony and Cosmology.- Velocity of gravitational contraction of a gaseous sphere.- Bifurcation of a dissipative system.- Electromagnetic energy radiation by a celestial body as an electric dipole.- Cosmo-chemical effects.- Direct derivation of the equation of virial oscillations from Einstein's equation.- 8. Global Dynamics of the Earth.- Problems of global dynamics in geophysics.- Unperturbed virial oscillations of the Earth.- Solution of Jacobi's virial equation for the Earth's atmosphere.- Perturbed oscillations of the Earth's atmosphere.- Identification of resonance frequencies.- Observation of the virial eigenoscillations of the Earth's atmosphere.- Conclusion.- References.