Optimal Control and Geometry: Integrable Systems

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book Optimal Control and Geometry: Integrable Systems by Velimir Jurdjevic, Cambridge University Press
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Author: Velimir Jurdjevic ISBN: 9781316585795
Publisher: Cambridge University Press Publication: July 4, 2016
Imprint: Cambridge University Press Language: English
Author: Velimir Jurdjevic
ISBN: 9781316585795
Publisher: Cambridge University Press
Publication: July 4, 2016
Imprint: Cambridge University Press
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

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