Jacobi dynamics : many-body problems in integral characteristics / V.I. Ferronsky, S.A. Denisik, S.V. Ferronsky.

Format:

Book

Author/Creator:

Ferronskiĭ, V. I. (Vasiliĭ Ivanovich)

Contributor:

Denisov, S. A. (Sergeĭ Alekseevich)

Ferronskiĭ, S. V.

Series:

Astrophysics and space science library.

Astrophysics and space science library

Language:

English

Subjects (All):

Many-body problem.

Dynamics.

Hamilton-Jacobi equations.

Astrophysics.

Physical Description:

1 online resource (337 p.)

Edition:

2nd ed.

Place of Publication:

Dordrecht : Springer Science, 2011.

Language Note:

English

Summary:

In their approach to Earth dynamics the authors consider the fundamentals of Jacobi Dynamics (1987, Reidel) for two reasons. First, because satellite observations have proved that the Earth does not stay in hydrostatic equilibrium, which is the physical basis of today’s treatment of geodynamics. And secondly, because satellite data have revealed a relationship between gravitational moments and the potential of the Earth’s outer force field (potential energy), which is the basis of Jacobi Dynamics. This has also enabled the authors to come back to the derivation of the classical virial theorem and, after introducing the volumetric forces and moments, to obtain a generalized virial theorem in the form of Jacobi’s equation. Thus a physical explanation and rigorous solution was found for the famous Jacobi’s equation, where the measure of the matter interaction is the energy. The main dynamical effects which become understandable by that solution can be summarized as follows: • the kinetic energy of oscillation of the interacting particles which explains the physical meaning and nature of the gravitation forces; • separation of the shell’s rotation of a self-gravitating body with respect to the mass density; difference in angular velocities of the shell rotation; • continuity in changing the potential of the outer gravitational force field together with changes in density distribution of the interacting masses (volumetric center of masses); • the nature of the precession of the Earth, the Moon and satellites; the nature of the rotating body’s magnetic field and the generation of the planet’s electromagnetic field. As a final result, the creation of the bodies in the Solar System having different orbits was discussed. This result is based on the discovery that all the averaged orbital velocities of the bodies in the Solar System and the Sun itself are equal to the first cosmic velocities of their proto-parents during the evolution of their redistributed mass density. Audience The work is a logical continuation of the book Jacobi Dynamics and is intended for researchers, teachers and students engaged in theoretical and experimental research in various branches of astronomy (astrophysics, celestial mechanics and stellar dynamics and radiophysics), geophysics (physics and dynamics of the Earth’s body, atmosphere and oceans), planetology and cosmogony, and for students of celestial, statistical, quantum and relativistic mechanics and hydrodynamics.

Contents:

Jacobi Dynamics; Preface to the Second Edition; Preface to the First Edition; Contents; Chapter 1: Introduction: General Principles and Approaches in Dynamics; 1.1 Principle of Mutual Reversibility; 1.2 Action and Integral Canonical Pairs; 1.3 Integral Characteristics in the Study of Dynamics of Natural Systems; 1.3.1 Method of Moments: Specific Features in Integral Approach and First Moments; Chapter 2: Recent Observations and Understanding Physical Meaning of Jacobi ́s Virial Equation; 2.1 Dynamical Effects Discovered by Space Study

2.2 Interpretation of Satellite Orbits and Failure of Hydrostatic Equilibrium of the Earth and the Moon2.3 Imbalance Between the Earth ́s Potential and Kinetic Energy; 2.4 Generalization of Classical Virial Theorem; 2.5 Reduction of Inner Gravitational Field of a Body to the Resultant Envelope of Pressure; Chapter 3: Derivation of Jacobi ́s Virial Equation for Description of Dynamics of Natural Systems; 3.1 Derivation of Jacobi ́s Virial Equation from Newtonian Equations of Motion; 3.2 Derivation of a Generalized Jacobi ́s Virial Equation for Dissipative Systems

3.3 Derivation of Jacobi ́s Virial Equation from Eulerian Equations3.4 Derivation of Jacobi ́s Virial Equation from Hamiltonian Equations; 3.5 Derivation of Jacobi ́s Virial Equation in Quantum Mechanics; 3.6 General Covariant Form of Jacobi ́s Virial Equation; 3.7 Relativistic Analogue of Jacobi ́s Virial Equation; 3.8 Universality of Jacobi ́s Virial Equation for Description of Dynamics of Natural Systems; Chapter 4: Solution of Jacobi ́s Virial Equation for Conservative Systems; 4.1 Solution of Jacobi ́s Virial Equation in Classical Mechanics; 4.1.1 The Classical Approach

4.1.2 The Dynamic Approach4.2 Solution of the N-Body Problem in the Framework of Conservative System; 4.3 Solution of Jacobi ́s Virial Equation in Hydrodynamics; 4.3.1 The Hydrodynamic Approach; 4.3.2 The Virial Approach; 4.4 The Hydrogen Atom as a Quantum Mechanical Analogue of the Two-Body Problem; 4.5 Solution of a Virial Equation in the Theory of Relativity (Static Approach); Chapter 5: Perturbed Virial Oscillations of a System; 5.1 Analytical Solution of a Generalized Equation of Virial Oscillations; 5.2 Solution of the Virial Equation for a Dissipative System

5.3 Solution of the Virial Equation for a System with FrictionChapter 6: Relationship Between Jacobi Function and Potential Energy; 6.1 Asymptotic Limit of Simultaneous Collision of Mass Points for a Conservative System; 6.2 Asymptotic Limit of Simultaneous Collision of Mass Points for Non-conservative Systems; 6.3 Asymptotic Limit of Simultaneous Collision of Charged Particles of a System; 6.4 Relationship Between Jacobi Function and Potential Energy for a System with High Symmetry; 6.4.1 Systems with Spherical Symmetry; 6.4.2 Polytropic Gas Sphere Model

6.4.3 System with Elliptical Symmetry

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789400704985

9400704984

OCLC:

728101897