Order and Chaos in Dynamical AstronomyThere have been many books on Dynamical Astronomy up to now. Many are devoted to Celestial Mechanics, but there are also several books on Stellar and Galactic Dynamics. The first books on stellar dynamics dealt mainly with the statistics of stellar motions (e. g. Smart's "Stellar Dynamics" (1938), or Trumpler and Weaver's "Statistical Astronomy" (1953)). A classical book in this field is Chandrasekhar's "Principles of Stellar Dynamics" (1942) that dealt mainly with the time of relaxation, the solutions of Liouville's equation, and the dynamics of clusters. In the Dover edition of this book (1960) an extended Appendix was added, containing the statistical mechanics of stellar systems, a quite "modern" subject at that time. The need for a classroom book was covered for several years by the book of Mihalas and Routly "Galactic Astronomy" (1969). But the most complete book in this field is Binney and Tremaine's "Galactic Dynamics" (1987). This book covers well the classical topics of stellar dynamics, and many subjects of current interest. Another classical book in dynamical astronomy is the extensive 4-Volume treatise of Hagihara "Celestial Mechanics" (1970, 1972, 1974, 1975). In more recent years much progress has been made on new topics that are of vital interest for stellar and galactic dynamics. The main new topic is Chaos. The progress of the theory of chaos has influenced considerably the area of stellar and galactic dynamics. The study of order and chaos has provided a new dimension in dynamics. |
Contents
| 1 | |
| 11 | |
The Toda Lattice | 42 |
Distribution of Periodic Orbits | 318 |
Order and Chaos in Galaxies | 377 |
Order and Chaos | 539 |
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Common terms and phrases
4/1 resonance angle angular momentum Arnold diffusion Astr Astron Astrophys asymptotic curves axis axisymmetric box orbits calculations chaos chaotic domain chaotic orbits close considered Contopoulos corotation corresponding degrees of freedom deviation dynamical systems energy equation escape families of periodic frequencies Froeschlé function galactic galaxy Giorgilli Hamiltonian system Hénon higher order infinite infinity initial conditions integrals of motion intersections invariant curves islands of stability Kandrup Lagrangian points larger Lindblad resonance lobes Lyapunov characteristic number Lynden-Bell M₁ Mech method N-body N-body simulations nonlinear parameter particles periodic orbits perturbation phase space Phys plane Poincaré points potential problem regions rotation number Schwarzschild Sect self-consistent spectra spiral stable stars surface of section theorem theory third integral Toda lattice unstable orbits unstable periodic orbits V₁ variables velocity Voglis x-axis zero