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- DescriptionThe 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 n-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 BiographyProfessor Velimir Jurdjevic is one of the founders of geometric control theory. His pioneering work with H. J. Sussmann was deemed to be among the most influential papers of the century and his book, Geometric Control Theory, revealed the geometric origins of the subject and uncovered important connections to physics and geometry. It remains a major reference on non-linear control. Jurdjevic's expertise also extends to differential geometry, mechanics and integrable systems. His publications cover a wide range of topics including stability theory, Hamiltonian systems on Lie groups, and integrable systems. He has spent most of his professional career at the University of Toronto.
- Author(s)Velimir Jurdjevic
- PublisherCambridge University Press
- Date of Publication04/07/2016
- Series TitleCambridge Studies in Advanced Mathematics
- Series Part/Volume Number154
- Place of PublicationCambridge
- Country of PublicationUnited Kingdom
- ImprintCambridge University Press
- Content Note4 tables
- Weight740 g
- Width152 mm
- Height228 mm
- Spine27 mm
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