Optimal control and geometry : integrable systems [EBook] / Velimir Jurdjevic, University of Toronto.
Optimal control and geometry : integrable systems [EBook] / Velimir Jurdjevic, University of Toronto.
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...
Personal Name(s):  Jurdjevic, Velimir, (author) 

Imprint: 
Cambridge :
Cambridge University Press,
2016

Physical Description: 
1 online resource (xx, 415 pages) 
Note: 
englisch 
ISBN: 
9781107113886 9781316286852 
Series Title: 
Cambridge studies in advanced mathematics ;
154 
Subject (LOC):  
Full Text 
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 nonlinear 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. 