Hamiltonian systems with constraints: a geometric approach (Q911117)

Let \(M\) be a differential manifold and \(TM\), \(T^*M\) be its tangent and cotangent bundles. Under the Legendre transformation \(FL: TM\to T^*M\), if the image of \(FL\) is a proper submanifold of \(T^*M\), one obtains a Hamiltonian system with constraint. Then the corresponding equation of motion is the so-called Hamiltonian-Dirac equation. The author discusses first the local problem in which the image of \(FL\) is a submanifold of \(T^*M\) defined by the zeros of a finite family of functions. Then he turns to discuss the global problem in which the image of \(FL\) is any submanifold of \(T^*M\). In both cases the author proposes a new algorithm to obtain the constraint submanifold and the dynamical vector field on it. A simple example is given.