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# Jacobi Dynamics: Many-Body Problem in Integral Characteristics by S. V. Ferronsky, V. I. Ferronsky, S. A. Denisik (Paperback, 2011)

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## About this product

### Key Features

- Author(s)S. A. Denisik,S. V. Ferronsky,V. I. Ferronsky
- PublisherSpringer
- Date of Publication27/09/2011
- Language(s)English
- FormatPaperback
- ISBN-10940108629X
- ISBN-139789401086295
- GenreAstronomy, Space & Time
- Series TitleAstrophysics and Space Science Library
- Series Part/Volume Number130

### Publication Data

- Place of PublicationDordrecht
- Country of PublicationNetherlands
- ImprintSpringer
- Content Notebiography

### Dimensions

- Weight593 g
- Width156 mm
- Height234 mm
- Spine20 mm
- Pagination382

### Editorial Details

- Format DetailsTrade paperback (US)
- Edition StatementSoftcover reprint of the original 1st ed. 1987

### Description

- Table Of Contents1. 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.

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