Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.
Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.
Professor 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.
Inhaltsangabe
1. The orbit theorem and Lie determined systems 2. Control systems. Accessibility and controllability 3. Lie groups and homogeneous spaces 4. Symplectic manifolds. Hamiltonian vector fields 5. Poisson manifolds, Lie algebras and coadjoint orbits 6. Hamiltonians and optimality: the Maximum Principle 7. Hamiltonian view of classic geometry 8. Symmetric spaces and sub-Riemannian problems 9. Affine problems on symmetric spaces 10. Cotangent bundles as coadjoint orbits 11. Elliptic geodesic problem on the sphere 12. Rigid body and its generalizations 13. Affine Hamiltonians on space forms 14. Kowalewski-Lyapunov criteria 15. Kirchhoff-Kowalewski equation 16. Elastic problems on symmetric spaces: Delauney-Dubins problem 17. Non-linear Schroedinger's equation and Heisenberg's magnetic equation. Solitons.
1. The orbit theorem and Lie determined systems 2. Control systems. Accessibility and controllability 3. Lie groups and homogeneous spaces 4. Symplectic manifolds. Hamiltonian vector fields 5. Poisson manifolds, Lie algebras and coadjoint orbits 6. Hamiltonians and optimality: the Maximum Principle 7. Hamiltonian view of classic geometry 8. Symmetric spaces and sub-Riemannian problems 9. Affine problems on symmetric spaces 10. Cotangent bundles as coadjoint orbits 11. Elliptic geodesic problem on the sphere 12. Rigid body and its generalizations 13. Affine Hamiltonians on space forms 14. Kowalewski-Lyapunov criteria 15. Kirchhoff-Kowalewski equation 16. Elastic problems on symmetric spaces: Delauney-Dubins problem 17. Non-linear Schroedinger's equation and Heisenberg's magnetic equation. Solitons.
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