Optimal Control and Geometry: Integrable Systems
eBook - PDF

Optimal Control and Geometry: Integrable Systems

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eBook - PDF

Optimal Control and Geometry: Integrable Systems

Book details
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About This Book

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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Yes, you can access Optimal Control and Geometry: Integrable Systems by Velimir Jurdjevic in PDF and/or ePUB format, as well as other popular books in Matemáticas & Matemáticas general. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2016
ISBN
9781316587058
Topic
Matemáticas
Subtopic
Matemáticas general

Table of contents

  1. Cover
  2. Half-title
  3. Series information
  4. Title page
  5. Copyright information
  6. Table of contents
  7. Acknowledgments
  8. Introduction
  9. Chapter 1 The Orbit Theorem and Lie determined systems
  10. Chapter 2 Control systems: accessibility and controllability
  11. Chapter 3 Lie groups and homogeneous spaces
  12. Chapter 4 Symplectic manifolds: Hamiltonian vector fields
  13. Chapter 5 Poisson manifolds, Lie algebras, and coadjoint orbits
  14. Chapter 6 Hamiltonians and optimality: the Maximum Principle
  15. Chapter 7 Hamiltonian view of classic geometry
  16. Chapter 8 Symmetric spaces and sub-Riemannian problems
  17. Chapter 9 Affine-quadratic problem
  18. Chapter 10 Cotangent bundles of homogeneous spacesas coadjoint orbits
  19. Chapter 11 Elliptic geodesic problem on the sphere
  20. Chapter 12 Rigid body and its generalizations
  21. Chapter 13 Isometry groups of space forms and affine systems: Kirchhoff's elastic problem
  22. Chapter 14 Kowalewski–Lyapunov criteria
  23. Chapter 15 Kirchhoff–Kowalewski equation
  24. Chapter 16 Elastic problems on symmetric spaces: the Delauney–Dubins problem
  25. Chapter 17 The non-linear Schroedinger's equation and Heisenberg's magnetic equation–solitons
  26. References
  27. Index