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arXiv · 1006.3632

Constrained variational calculus: the second variation (part I)

Enrico Massa·Danilo Bruno·Gianvittorio Luria·Enrico Pagani
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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.

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Enrico Massa, Danilo Bruno, Gianvittorio Luria, Enrico Pagani. 2010-06-18. Constrained variational calculus: the second variation (part I). https://arxiv.org/abs/1006.3632

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