Hamiltonian Mechanics pp 167-172 | Cite as

# Symmetries and Topology of Dynamical Systems with two Degrees of Freedom

Chapter

## Abstract

Let
are local coordinates in

*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,$$ x = \left( {{q_1},{q_2},{p_1},{p_2}} \right) $$

*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
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## References

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© Springer Science+Business Media New York 1994