On the gauge structure of the calculus of variations with constraints
International Journal of Geometric Methods in Modern Physics, 2011•World Scientific
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.
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.
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.
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