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Jacobi dynamics : many-body problem in integral characteristics

Author: V I Ferronskiĭ; S A Denisov; S V Ferronskiĭ
Publisher: Dordrecht ; Boston : D. Reidel Pub. Co. ; Norwell, MA, U.S.A. : Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, ©1987.
Series: Astrophysics and space science library, v. 130.
Edition/Format:   Print book : EnglishView all editions and formats
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This book sets forth and builds upon the fundamentals of the dynamics of natural systems in formulating the problem presented by Jacobi in his famous lecture series "Vorlesungen tiber Dynamik"  Read more...

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Document Type: Book
All Authors / Contributors: V I Ferronskiĭ; S A Denisov; S V Ferronskiĭ
ISBN: 9027724180 9789027724182
OCLC Number: 14904932
Description: xi, 365 pages : illustrations ; 25 cm.
Contents: 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.- The classical approach.- The integral approach.- General case of conservative systems.- Solution of Jacobi's virial equation in hydrodynamics.- The hydrodynamic approach.- The integral approach.- 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.- Relationship between Jacobi function and potential energy for a system with high symmetry..- System with spherical symmetry.- Polytropic gas sphere model.- System with elliptical symmetry.- System with charged particles.- 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.- Lyapunov stability of motion of a system described in terms of co-ordinates and integral characteristics.- Stability of virial oscillations according to Lyapunov.- Stability of virial oscillations of celestial bodies as dissipative systems.- 7. Applications in Astrophysics, Cosmogony and Cosmology.- Velocity of gravitational contraction of a gaseous sphere.- Equilibrium boundary conditions for a gravitating gaseous sphere.- Relationship between potential and rotational energies of a rotating gaseous sphere.- limiting value of angular momentum of a contracting gaseous sphere.- Velocity of gravitational contraction of a gaseous sphere.- The luminosity-mass relationship.- 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.- The differential approach.- The integral approach.- 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.
Series Title: Astrophysics and space science library, v. 130.
Responsibility: by V.I. Ferronsky and S.A. Denisik and S.V. Ferronsky.
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`It is stimulating and resourceful reading for the astronomer, geophycist, or for any physically oriented scientists who sees his research subject placed within the framework of global natural Read more...

 
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