Optimal Control and Geometry: Integrable Systems (Hardcover)

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.