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Symmetries and Topology of Dynamical Systems with two Degrees of Freedom

  • Valery Kozlov
Part of the NATO ASI Series book series (NSSB, volume 331)

Abstract

Let M be a closed two-dimensional surface viewed as a configuration space of a dynamical system with two degrees of freedom. We denote the local coordinates on M by q 1, q 2. In mechanics they are usually called the generalized coordinates. Let p 1, p 2 be canonical momenta conjugated with q 1, q 2. Hence,
$$ x = \left( {{q_1},{q_2},{p_1},{p_2}} \right) $$
are local coordinates in the phase space T*M (the cotangent bundle of the surface M).

Keywords

Cotangent Bundle Geodesic Flow Positive Definite Quadratic Form Quadratic Integral Symmetry Field 
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 Science+Business Media New York 1994

Authors and Affiliations

  • Valery Kozlov
    • 1
  1. 1.Department of Mathematics and MechanicsMoscow State UniversityMoscowRussia

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