Constrained variational calculus: the second variation (part I)

2010/06/18 by Enrico Massa, Massa, Enrico, Danilo Bruno +5 · 1 citation
Mathematics · Physics and Astronomy · #37J #49J #70F25 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:37J #msc:49J #msc:70F25

paper · pdf · doi:10.48550/arxiv.1006.3632

arxiv created 2012/10/16 · arxiv updated 2012/10/17

Abstract

Within the geometrical framework developed in arXiv:0705.2362, the problem of minimality for constrained calculus of variations is analysed among the class of differentiable curves. A fully covariant representation of the second variation of the action functional, based on a suitable gauge transformation of the Lagrangian, is explicitly worked out. Both necessary and sufficient conditions for minimality are proved, and are then reinterpreted in terms of Jacobi fields.

Citations

• Geometric control theory I: mathematical foundations

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• Inexact calculus of variations on the hyperspherical tangent bundle with connections to the attention mechanism

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