Singular Lagrangian Systems on Jet Bundles

Abstract

The jet bundle description of time-dependent mechanics is revisited. The constraint algorithm for singular Lagrangians is discussed and an exhaustive description of the constraint functions is given. By means of auxiliary connections we give a basis of constraint functions in the Lagrangian and Hamiltonian sides. An additional description of constraints is also given considering at the same time compatibility, stability and second-order condition problems. Finally, a classification of the constraints in first and second class is obtained using a cosymplectic geometry setting. Using the second class constraints, a Dirac bracket is introduced, extending the well-known construction by Dirac.

65 pages. LaTeX file

References in corpus (2)

• On the Multimomentum Bundles and the Legendre Maps in Field Theories
• Constraints in polysymplectic (covariant) Hamiltonian formalism

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