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Singular Lagrangian Systems on Jet Bundles | M. de León
; J. Mar’{i}n-Solano
; J.C. Marrero
; M.C. Mu~noz-Lecanda
; N. Román-Roy
; | Date: |
10 May 2001 | Journal: | Fortsch.Phys. 50 (2002) 105-169 | Subject: | Mathematical Physics; Differential Geometry; Symplectic Geometry MSC-class: 37C10; 37J05; 53C05; 53D05; 55R10; 58A20; 70G45; 70H03; 70H05; 70H45 | math-ph math.DG math.MP math.SG | 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. | Source: | arXiv, math-ph/0105012 | Services: | Forum | Review | PDF | Favorites |
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