Titlebook: Mathematical Aspects of Classical and Celestial Mechanics; Vladimir I. Arnold,Valery V. Kozlov,Anatoly I. Nei Book 2006Latest edition Spri

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978-3-642-06647-4Springer-Verlag Berlin Heidelberg 2006

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WAIL

The n-Body Problem,Suppose that two points (., .) and (., .) interact with each other with potential energy .(|. - .|), so that the equations of motion have the form

Introduction

Symmetry Groups and Order Reduction,Let (., .) be a Lagrangian system and . a smooth field on .. The field . gives rise to the one-parameter group . of diffeomorphisms . : . → . defined by the differential equation

Defense

Variational Principles and Methods,One of the fundamental objects of classical mechanics is a Lagrangian system - a pair (., .), where . is a smooth manifold (the configuration space of the mechanical system), and . a smooth function on the tangent bundle . (the Lagrange function or Lagrangian).