Hamiltonian Systems in Phase Space

  • Chao-Cheng Wang
Part of the Mathematical Concepts and Methods in Science and Engineering book series (MCSENG, volume 16)


The equations of Lagrange, which we have derived in Chapter 1, may be transformed into a system of first-order differential equations when the generalized force possesses a potential function. The transformation is known as the Legendre transformation and the resulting first-order system is known as the Hamiltonian system. In this chapter we develop the theory of Hamiltonian systems from the standpoint of a flow problem and in the context of a certain first-order partial differential equation known as the Hamilton-Jacobi equation.


Hamiltonian System Hamiltonian Function Legendre Transformation Solution Surface Contact Transformation 
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Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • Chao-Cheng Wang
    • 1
  1. 1.Rice UniversityHoustonUSA

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