an:04143082
Zbl 0697.58019
Mu??oz Lecanda, M. C.
Hamiltonian systems with constraints: a geometric approach
EN
Int. J. Theor. Phys. 28, No. 11, 1405-1417 (1989).
00173378
1989
j
70H45 70G45 37J99
Hamiltonian system; Hamiltonian-Dirac equation
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.
Guizhang Tu