Abstract
An integrable variant of a nonholonomic Suslov problem with compact and noncompact levels of the energy integral is investigated. The integral manifolds can be both compact and noncompact two-dimensional surfaces, in particular, a torus with four holes, a sphere with four holes, and a sphere with a number of handles and a number of holes. The surgeries of noncompact integral manifolds of integrable Hamiltonian systems are also considered. A generalization of the Reeb graph is proposed for noncompact case.
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