Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed 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 reinterpreted in terms of Jacobi fields.
Geometric constrained variational calculus. II: The second variation (Parti I) / Massa, Enrico; Bruno, Danilo; Luria, Gianvittorio; Pagani, Enrico. - In: INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS. - ISSN 0219-8878. - STAMPA. - 2015 Vol. 12:12(2015), pp. 1-31. [10.1142/S0219887815501327]
Geometric constrained variational calculus. II: The second variation (Parti I)
Pagani, Enrico
2015-01-01
Abstract
Within the geometrical framework developed in [Geometric constrained variational calculus. I: Piecewise smooth extremals, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550061], the problem of minimality for constrained calculus of variations is analyzed 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 reinterpreted in terms of Jacobi fields.| File | Dimensione | Formato | |
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