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28 March 2024
 
  » arxiv » math-ph/0105012

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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
AbstractThe 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
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