ON THE GAUGE STRUCTURE OF THE CALCULUS OF VARIATIONS WITH CONSTRAINTS

被引：2

作者：

Bruno, Danilo ^{[1
]}

Luria, Gianvittorio ^{[2
]}

Pagani, Enrico ^{[3
]}

机构：

[1] Univ Genoa, Dipartimento Matemat, I-16146 Genoa, Italy

[2] Univ Genoa, DIPTEM Sez Metodi & Modelli Matemat, I-16129 Genoa, Italy

[3] Univ Trent, Dipartimento Matemat, I-38050 Povo, Italy

来源：

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS | 2011年 / 8卷 / 08期

关键词：

Constrained calculus of variations; optimal control theory; gauge theory; first variation; MECHANICS;

D O I：

10.1142/S0219887811005890

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页码：1723 / 1746

页数：24

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