The theory of Pontryagin minimum is developed for problems in the calculus of variations. The application of the notion of Pontryagin minimum to the calculus of variations is a distinctive feature of the book. A new theory of quadratic conditions for a Pontryagin minimum, which covers broken extremals, is developed, and corresponding sufficient conditions for a strong minimum are obtained Some classical theorems of the calculus of variations are generalized.
The book can be used by researchers and graduate students in mathematics working In the calculus of variations and control theory, and in applications to mechanics, physics, and engineering.