Control Theory And Transformation Methods In Classical Mechanics

Within the framework of the Hamiltonian description of dynamical systems, canonical transformations and Hamilton-Jacobi theory are examined from the control perspective. For canonical transformations, conditions on the transformation Jacobian matrices are derived such that an equivalent linear (Brunovsky form) representation of nonlinear systems is obtained. Hamilton-Jacobi theory is used to parametrize the solution of the equations of motion in terms of the control variable.