A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the “Lagrangian” L is replaced by a section of a suitable principal fiber bundle over the velocity space. A geometric rephrasement of Pontryagin’s maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved.

On the Gauge structure of the calculus of variations with constraints

Pagani, Enrico
2011-01-01

Abstract

A gauge-invariant formulation of constrained variational calculus, based on the introduction of the bundle of affine scalars over the configuration manifold, is presented. In the resulting setup, the “Lagrangian” L is replaced by a section of a suitable principal fiber bundle over the velocity space. A geometric rephrasement of Pontryagin’s maximum principle, showing the equivalence between a constrained variational problem in the state space and a canonically associated free one in a higher affine bundle, is proved.
2011
8
D., Bruno; G., Luria; Pagani, Enrico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/85718
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