Central Configurations, Periodic Orbits, and Hamiltonian Systems
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1 The Averaging Theory for Computing Periodic Orbits.- Introduction: the classical theory.- Averaging theory for arbitrary order and dimension.- Three applications of Theorem.- 2 Lectures on Central Configurations.- The n-body problem.- Symmetries and integrals.- Central configurations and self-similar solutions.- Matrix equations of motion.- Homographic motions of central configurations in Rd.- Albouy-Chenciner reduction and relative equilibria in Rd.- Homographic motions in Rd.- Central configurations as critical points.- Collinear central configurations.- Morse indices of non-collinear central configurations.- Morse theory for CC's and SBC's.- Dziobek configurations.- Convex Dziobek central configurations.- Generic finiteness for Dziobek central configurations.- Some open problems.- 3 Dynamical Properties of Hamiltonian Systems.- Introduction.- Low dimension.- Some theoretical results, their implementation and practical tools.- Applications to Celestial Mechanics.
Format:Paperback
Language:English
ISBN:3034809328
ISBN13:9783034809320
Release Date:December 2015
Publisher:Birkhauser
Length:232 Pages
Weight:0.87 lbs.
Dimensions:0.5" x 6.7" x 9.6"
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