Jacobi Dynamics (eBook)
XIV, 330 Seiten
Springer Netherland (Verlag)
978-94-007-0498-5 (ISBN)
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.
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. AudienceThe 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.
Preface to the Second Edition 6
Preface to the First Edition 8
Contents 12
Chapter 1: Introduction: General Principles and Approaches in Dynamics 16
1.1 Principle of Mutual Reversibility 17
1.2 Action and Integral Canonical Pairs 22
1.3 Integral Characteristics in the Study of Dynamics of Natural Systems 30
1.3.1 Method of Moments: Specific Features in Integral Approach and First Moments 37
Chapter 2: Recent Observations and Understanding Physical Meaning of Jacobi´s Virial Equation 45
2.1 Dynamical Effects Discovered by Space Study 45
2.2 Interpretation of Satellite Orbits and Failure of Hydrostatic Equilibrium of the Earth and the Moon 49
2.3 Imbalance Between the Earth´s Potential and Kinetic Energy 56
2.4 Generalization of Classical Virial Theorem 57
2.5 Reduction of Inner Gravitational Field of a Body to the Resultant Envelope of Pressure 64
Chapter 3: Derivation of Jacobi´s Virial Equation for Description of Dynamics of Natural Systems 70
3.1 Derivation of Jacobi´s Virial Equation from Newtonian Equations of Motion 71
3.2 Derivation of a Generalized Jacobi´s Virial Equation for Dissipative Systems 79
3.3 Derivation of Jacobi´s Virial Equation from Eulerian Equations 82
3.4 Derivation of Jacobi´s Virial Equation from Hamiltonian Equations 89
3.5 Derivation of Jacobi´s Virial Equation in Quantum Mechanics 91
3.6 General Covariant Form of Jacobi´s Virial Equation 99
3.7 Relativistic Analogue of Jacobi´s Virial Equation 101
3.8 Universality of Jacobi´s Virial Equation for Description of Dynamics of Natural Systems 104
Chapter 4: Solution of Jacobi´s Virial Equation for Conservative Systems 106
4.1 Solution of Jacobi´s Virial Equation in Classical Mechanics 107
4.1.1 The Classical Approach 107
4.1.2 The Dynamic Approach 111
4.2 Solution of the N-Body Problem in the Framework of Conservative System 113
4.3 Solution of Jacobi´s Virial Equation in Hydrodynamics 118
4.3.1 The Hydrodynamic Approach 118
4.3.2 The Virial Approach 122
4.4 The Hydrogen Atom as a Quantum Mechanical Analogue of the Two-Body Problem 124
4.5 Solution of a Virial Equation in the Theory of Relativity (Static Approach) 132
Chapter 5: Perturbed Virial Oscillations of a System 135
5.1 Analytical Solution of a Generalized Equation of Virial Oscillations 137
5.2 Solution of the Virial Equation for a Dissipative System 144
5.3 Solution of the Virial Equation for a System with Friction 147
Chapter 6: Relationship Between Jacobi Function and Potential Energy 150
6.1 Asymptotic Limit of Simultaneous Collision of Mass Points for a Conservative System 151
6.2 Asymptotic Limit of Simultaneous Collision of Mass Points for Non-conservative Systems 153
6.3 Asymptotic Limit of Simultaneous Collision of Charged Particles of a System 167
6.4 Relationship Between Jacobi Function and Potential Energy for a System with High Symmetry 172
6.4.1 Systems with Spherical Symmetry 173
6.4.2 Polytropic Gas Sphere Model 177
6.4.3 System with Elliptical Symmetry 182
6.4.4 System with Charged Particles 187
Chapter 7: Applications in Celestial Mechanics and Geodynamics 194
7.1 The Problem of Eigenoscillations of a Celestial Body 195
7.1.1 Hydrostatic Approach 195
7.1.2 Dynamic Approach 200
7.2 Structure of Potential and Kinetic Energies of a Non-uniform Body 205
7.3 Equations of Dynamical Equilibrium of Oscillation and Rotation of a Body 207
7.4 Equations of Oscillation and Rotation of a Body and Their Solution 208
7.5 Application of Roche´s Tidal Approach for Separation of the Body Shells 212
7.6 Physical Meaning of Archimedes and Coriolis Forces and Separation of the Earth´s Shells 213
7.7 Self-similarity Principle and the Radial Component of a Non-uniform Sphere 214
7.8 Charges-Like Motion of Non-uniformities and Tangential Component of the Force Function 216
7.9 Radial Distribution of Mass Density and the Body´s Inner Force Field 218
7.10 Oscillation Frequency and Angular Velocity of the Earth´s Shell Rotation 226
7.10.1 Thickness of the Upper Earth´s Rotating Shell 227
7.10.2 Oscillation of the Earth´s Shells 228
7.10.3 Angular Velocity of Shell Rotation 229
7.11 Perturbation Effects Studied on Basis of Dynamic Equilibrium 230
7.11.1 The Nature of Perturbation for Orbital Motion of a Body 230
7.11.2 Change of the Outer Force Field and the Nature of Precession and Nutation 233
7.11.3 Observed Picture of a Body Precession 235
7.11.4 The Nature of Precession and Nutation 235
7.11.5 The Nature of Possible Clockwise Rotation of the Outer Core of the Earth 236
7.11.6 The Nature of the Force Field Potential Change 238
7.11.7 The Nature of the Earth´s Orbit Plane Obliquity 238
7.11.8 The Nature of Chandler´s Effect of the Earth Pole Wobbling 238
7.11.9 Change in Climate as an Effect of Rotation of the Earth´s Shells 239
7.11.10 The Nature of Obliquity of the Earth´s Equatorial Plane to the Ecliptic 239
7.11.11 Tidal Interaction of Two Bodies 240
7.12 Dynamics of the Earth´s Atmosphere and Ocean 241
7.12.1 Derivation of the Virial Equation for the Earth´s Atmosphere 242
7.12.2 Non-perturbed Oscillation of the Atmosphere 246
7.12.3 Perturbed Oscillations 249
7.12.4 Resonance Oscillation 253
7.12.5 Observation of the Virial Eigenoscillations of the Earth´s Atmosphere 256
7.12.6 Dynamics of the Oceans 264
7.12.7 The Nature of the Weather and Climate Changes 264
7.13 Lyapunov Stability of Motion in Jacobi Dynamics 267
7.13.1 Lyapunov Stability of Motion of a System Described in Terms of Co-ordinates and Integral Characteristics 267
7.13.2 Stability of Virial Oscillations According to Lyapunov 274
7.13.3 Stability of Virial Oscillations of Celestial Bodies as Dissipative Systems 277
Chapter 8: Creation and Evolution of the Solar System Bodies 278
8.1 The Third Kepler´s Law as a Kinematics Basis for the Problem Solution of Creation of the Solar System Bodies 279
8.2 Evolution by Radiation and Gravitational Contraction of a Gaseous Sphere 285
8.2.1 Equilibrium Boundary Conditions for a Gravitating Gaseous Sphere 286
8.2.2 Velocity of Gravitational Contraction of a Gaseous Sphere 288
8.2.3 The Luminosity-Mass Relationship 294
8.2.4 Bifurcation of a Dissipative System 296
8.3 Cosmo-Chemical Effects 299
8.4 Direct Derivation of the Equation of Virial Oscillation from Einstein´s Equation 302
Chapter 9: The Nature of Electromagnetic Field of a Celestial Body and Mechanism of Its Energy Generation 308
9.1 Electromagnetic Component of the Interacted Masses 309
9.2 Potential Energy of the Coulomb Interaction of Mass Particles 311
9.3 Emission of Electromagnetic Energy by a Celestial Body as an Electric Dipole 311
9.4 Quantum Effects of Generated Electromagnetic Energy 316
9.5 The Nature of the Star Emitted Radiation Spectrum 318
9.6 Temperature of the Relict Radiation 319
Chapter 10: Conclusions 321
References 330
Index 332
| Erscheint lt. Verlag | 11.4.2011 |
|---|---|
| Reihe/Serie | Astrophysics and Space Science Library |
| Zusatzinfo | XIV, 330 p. |
| Verlagsort | Dordrecht |
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Geowissenschaften ► Geografie / Kartografie |
| Naturwissenschaften ► Geowissenschaften ► Geophysik | |
| Naturwissenschaften ► Physik / Astronomie ► Astronomie / Astrophysik | |
| Technik | |
| Schlagworte | Dynamical equilibrium • Hydrostatic equilibrium • Jacobi dynamics • Remote Sensing/Photogrammetry • Self-gravitating body • Shell separation |
| ISBN-10 | 94-007-0498-4 / 9400704984 |
| ISBN-13 | 978-94-007-0498-5 / 9789400704985 |
| Haben Sie eine Frage zum Produkt? |
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