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Basic Principles of Classical Mechanics

  • Vladimir I. Arnold
  • Valery V. Kozlov
  • Anatoly I. Neishtadt
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 3)

Abstract

For describing the motion of a mechanical system various mathematical models are used based on different “principles” - laws of motion. In this chapter we list the basic objects and principles of classical dynamics. The simplest and most important model of the motion of real bodies is Newtonian mechanics, which describes the motion of a free system of interacting points in threedimensional Euclidean space. In § 1.6 we discuss the suitability of applying Newtonian mechanics when dealing with complicated models of motion.

Keywords

Poisson Bracket Inertial Frame Symplectic Structure Classical Mechanics Lagrangian System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2006

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  • Valery V. Kozlov
    • 3
    • 4
  • Anatoly I. Neishtadt
    • 5
    • 6
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité Paris 9 - DauphineFrance
  3. 3.Steklov Mathematical InstituteMoscowRussia
  4. 4.Department of Mathematics and MechanicsLomonosov Moscow State UniversityMoscowRussia
  5. 5.Space Research InstituteMoscowRussia
  6. 6.Department of Mathematics and MechanicsLomonosov Moscow State UniversityMoscowRussia

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