The paper deals with integrable systems related to Hamiltonian \(G\)-actions. Within the framework of noncommutative integrability, collective motion, reduced and partial integrability are studied. The case of reduction of Hamiltonian flows restricted to invariant submanifolds is studied also. Typically, the invariant submanifold is foliated on invariant tori, but motion is not quasi-periodic. The classical example is the classical Hess-Appel’rot case of the rigid body motion.
Contents: 1. Introduction. 2. Noncommutative Integrability. 3. Symmetries and Reductions. 4. Integrable Systems Related to Hamiltonian Actions. 5. Reductions and Integrability. 6. Partial Integrability. 84 References.