Canonical theories of Langrangian dynamical systems in physics

Canonical theories of Langrangian dynamical systems in physics By reformulating the variational problem for a given classical Lagrangian field theory in the framework of differential forms, one can show (Lepage) that for m a2 independent and for n2 dependent (field) variables z" =f(x) a much wider variety of Legendre transformations v% - ditf(x)-*Pa, L^H, exists than has been employed in physics. The different canonical theories for a given Lagrangian can be classified according to the rank of the corresponding basic canonical m-form. Each such canonical theory leads to a Hamilton-Jacobi theory, the "wave fronts" of which are transversal to solutions of the field equations. Two canonical theories are discussed in more detail: The one by DeDonder and Weyl which employs the conventional canonical momenta pi = d

Authors: Kastrup H.A.Pages: 167     Year: 1983

Tags: canonical langrangian theories systems dynamical physics

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