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Hamiltonian systems with constraints: a geometric approach. (English) Zbl 0697.58019
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.
Reviewer: Guizhang Tu

MSC:
 70H45 Constrained dynamics, Dirac’s theory of constraints 70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:
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