Linear Almost Poisson Structures and Hamilton-jacobi Theory. Applications to Nonholonomic Mechanics

  title={Linear Almost Poisson Structures and Hamilton-jacobi Theory. Applications to Nonholonomic Mechanics},
  author={Manuel de Le{\'o}n and Juan C. Marrero and David Mart{\'i}n de Diego}
In this paper, we study the underlying geometry in the classical Hamilton-Jacobi theory. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear almost Poisson structure and a Hamiltonian function, both on the dual bundle (a Hamiltonian system). From them, it is possible to formulate the Hamilton-Jacobi theory, obtaining as a particular case, the classical theory. The main application in this paper arises… CONTINUE READING

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