Ebook: Theory of Orbits: Perturbative and Geometrical Methods
- Tags: Astronomy Observations and Techniques, Statistical Physics Dynamical Systems and Complexity, Extraterrestrial Physics Space Sciences, Geophysics/Geodesy
- Series: Astronomy and Astrophysics Library
- Year: 1999
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large N-body systems are illustrated.
Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large N-body systems are illustrated.
Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large N-body systems are illustrated.
Content:
Front Matter....Pages I-XV
Classical Perturbation Theory in Celestial Mechanics. The Equations of Planetary Motion....Pages 1-67
Canonical Perturbation Theory....Pages 69-123
Lie Transform Perturbation Theory....Pages 125-178
The Theory of Adiabatic Invariants....Pages 179-233
Periodic Orbits and Resonances....Pages 235-295
Chaos....Pages 297-354
Numerical Experiments....Pages 355-397
Back Matter....Pages 399-423
Theory of Orbits treats celestial mechanics as well as stellar dynamics from the common point of view of orbit theory, making use of concepts and techniques from modern geometric mechanics. It starts with elementary Newtonian mechanics and ends with the dynamics of chaotic motion. The two volumes are meant for students in astronomy and physics alike. Prerequisite is a physicist's knowledge of calculus and differential geometry.
The first three chapters of this second volume are devoted to the theory of perturbations, starting from classical problems and arriving at the KAM theory, and to the introduction of the use of the Lie transform. A whole chapter treats the theory of adiabatic invariants and its applications in celestial mechanics and stellar dynamics. Also the theory of resonances is illustrated and applications in both fields are shown. Classical and modern problems connected to periodic solutions are reviewed. The description of modern developments of the theory of chaos in conservative systems is the subject of a chapter in which an introduction is given to what happens in both near-integrable and non-integrable systems. The invaluable help provided by computers in the exploration of the long-time behaviour of dynamical systems is acknowledged in a final chapter, where some numerical algorithms and their applications both to systems with few degrees of freedom and to large N-body systems are illustrated.
Content:
Front Matter....Pages I-XV
Classical Perturbation Theory in Celestial Mechanics. The Equations of Planetary Motion....Pages 1-67
Canonical Perturbation Theory....Pages 69-123
Lie Transform Perturbation Theory....Pages 125-178
The Theory of Adiabatic Invariants....Pages 179-233
Periodic Orbits and Resonances....Pages 235-295
Chaos....Pages 297-354
Numerical Experiments....Pages 355-397
Back Matter....Pages 399-423
....