Author | Meyer, Kenneth R. author |
---|---|

Title | Introduction to Hamiltonian Dynamical Systems and the N-Body Problem [electronic resource] / by Kenneth R. Meyer, Glen R. Hall |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1992 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-4073-8 |

Descript | XII, 294 p. online resource |

SUMMARY

This text grew out of graduate level courses in mathematics, engineering and physics given at several universities. The courses took students who had some background in differential equations and lead them through a systematic grounding in the theory of Hamiltonian mechanics from a dynamical systems point of view. Topics covered include a detailed discussion of linear Hamiltonian systems, an introduction to variational calculus and the Maslov index, the basics of the symplectic group, an introduction to reduction, applications of Poincarรฉ's continuation to periodic solutions, the use of normal forms, applications of fixed point theorems and KAM theory. There is a special chapter devoted to finding symmetric periodic solutions by calculus of variations methods. The main examples treated in this text are the N-body problem and various specialized problems like the restricted three-body problem. The theory of the N-body problem is used to illustrate the general theory. Some of the topics covered are the classical integrals and reduction, central configurations, the existence of periodic solutions by continuation and variational methods, stability and instability of the Lagrange triangular point. Ken Meyer is an emeritus professor at the University of Cincinnati, Glen Hall is an associate professor at Boston University, and Dan Offin is a professor at Queen's University

CONTENT

I. Hamiltonian Differential Equations and the N-Body Problem -- II. Linear Hamiltonian Systems -- III. Exterior Algebra and Differential Forms -- IV. Symplectic Transformations and Coordinates -- V. Introduction to the Geometric Theory of Hamiltonian Dynamical Systems -- VI. Continuation of Periodic Solutions -- VII. Perturbation Theory and Normal Forms -- VIII. Bifurcations of Periodic Orbits -- IX. Stability and KAM Theory -- X. Twist Maps and Invariant Curves -- References

Mathematics
Mathematical analysis
Analysis (Mathematics)
Physics
Mathematics
Analysis
Theoretical Mathematical and Computational Physics