Katarzyna Grabowska and Janusz Grabowski 2008 J. Phys. A: Math. Theor. 41 175204 doi:10.1088/1751-8113/41/17/175204
Variational calculus with constraints on general algebroids
Katarzyna Grabowska1 and Janusz Grabowski2
Show affiliationsVariational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler–Lagrange equations. Constrained systems are introduced in the variational and geometrical settings. The constrained Euler–Lagrange equations are derived for analogs of holonomic, vakonomic and nonholonomic constraints. This general model covers the majority of first-order Lagrangian systems which are present in the literature and reduces to the standard variational calculus and the Euler–Lagrange equations in classical mechanics for E = TM.
- PACS
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45.05.+x General theory of classical mechanics of discrete systems
45.10.Db Variational and optimization methods
- MSC
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17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
- Subjects
- Dates
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Issue 17 (2 May 2008)
Received 8 January 2008, in final form 5 March 2008
Published 15 April 2008
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Variational calculus with constraints on general algebroids
Katarzyna Grabowska and Janusz Grabowski 2008 J. Phys. A: Math. Theor. 41 175204
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