Suitable for advanced undergraduates and graduate students, this text surveys the classical theory of the calculus of variations. Topics include static systems, control systems, additional constraints, the Hamilton-Jacobi equation, and the accessory optimization problem. Emphasis throughout the text is placed upon methods and principles, which are illustrated by worked problems and sets of exercises. 1975 edition.
This book is, without doubt, one of the best mathematics books I have read. It guides you through the theory behind many important topics of the calculus of variations and optimal control while giving plenty of really good examples so that you can understand and apply what you have learned.
When I was buying it I couldn't believe that there wasn't much information or reviews about it. I bought it because I really liked its content, and now I'm astonished by how good it is. Totally recommend it!
PD: Many of the topics covered here are being taught in the edX course "Underactuated robotics", and are used by the MIT Robot Locomotion Group to build the control systems for the ATLAS humanoid robot.