Optimal Control and Geometry: Integrable Systems (Hardcover) (ISBN-13: 9781107113886)

The synthesis of symplectic geometry, the calculus of variations and control theory offered in this book provides a crucial foundation for the understanding of many problems in applied mathematics. Focusing on the theory of integrable systems, this book introduces a class of optimal control problems on Lie groups, whose Hamiltonians, obtained through the Maximum Principle of optimality, shed new light on the theory of integrable systems. These Hamiltonians provide an original and unified account of the existing theory of integrable systems. The book particularly explains much of the mystery surrounding the Kepler problem, the Jacobi problem and the Kovalevskaya Top. It also reveals the ubiquitous presence of elastic curves in integrable systems up to the soliton solutions of the non-linear Schroedinger's equation. Containing a useful blend of theory and applications, this is an indispensable guide for graduates and researchers in many fields, from mathematical physics to space control.

Author: Velimir Jurdjevic
ISBN-10: 1107113881
ISBN-13: 9781107113886
Publisher: Cambridge University Press
Language: English
Published: 07/04/2016
Pages: 423
Format: Hardcover
Weight: 1.60lbs
Size: 9.37h x 6.07w x 1.14d