Hamiltonian Systems in Phase Space
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.
KeywordsHamiltonian System Hamiltonian Function Legendre Transformation Solution Surface Contact Transformation
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