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Bifurcation sets in a problem on motion of a rigid body in fluid and in the generalization of this problem. (English) Zbl 0926.70009

Summary: We describe topology of energy surfaces and bifurcation sets for the classical Chaplygin problem and for its generalization. We also describe bifurcations of Liouville tori and calculate the Fomenko invariant (for the classical case this result is obtained analytically, and for the generalized case it is obtained with the help of computer modeling). Topological analysis shows that some topological characteristics (such as the form of the bifurcation set) change continuously, and some of them (such as topology of energy surfaces) change drastically as one of the first integrals (area integral) tends to zero.

MSC:

70E15 Free motion of a rigid body
70E50 Stability problems in rigid body dynamics
70G40 Topological and differential topological methods for problems in mechanics
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