Constrained variational calculus: the second variation (part I)
Mathematical Physics
2012-10-17 v3 math.MP
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.
Cite
@article{arxiv.1006.3632,
title = {Constrained variational calculus: the second variation (part I)},
author = {Enrico Massa and Danilo Bruno and Gianvittorio Luria and Enrico Pagani},
journal= {arXiv preprint arXiv:1006.3632},
year = {2012}
}