For 10 points, identify this two-word term from classical mechanics for a change of coordinates that preserves the form of Hamilton's equations.
If X is the two-by-two block matrix "zero, identity, negative identity, zero," then this type of function has a Jacobian J that satisfies the equation "J times X times J-transpose" equals "X," which is known as the symplectic condition. The active view of a system's time evolution considers a continuous succession of the infinitesimal type of these functions. The defining equation for these functions is typically written as "K equals H plus partial G partial t," where K and H are Hamiltonians and G is a generating function that may be any of four types depending on which displacements and conjugate momenta are used as independent variables. The volume of phase space and the value of the Poisson bracket are invariant with respect to these functions. For 10 points, identify this two-word term from classical mechanics for a change of coordinates that preserves the form of Hamilton's equations.
If X is the two-by-two block matrix "zero, identity, negative identity, zero," then this type of function has a Jacobian J that satisfies the equation "J times X times J-transpose" equals "X," which is known as the symplectic condition.
canonical transformations [accept mapping or change of coordinates for "transformation"; prompt on coordinate transformations or contact transformations or symplectomorphisms; do not accept "point transformations"]