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First integrals of motion equations of a generalized gyroscope in \(\mathbb R^n\). (Russian, English) Zbl 1127.70003

Vestn. Mosk. Univ., Ser. I 2003, No. 5, 37-41 (2003); translation in Mosc. Univ. Math. Bull. 58, No. 5, 25-29 (2003).
The authors study a generalized gyroscope in \(\mathbb R^n\) (see [W. von Frahm, Math. Ann. 8, 35–44 (1874; JFM 06.0198.01)]). The generalized gyroscope in \(\mathbb R^n\) is understood as a body with the following properties: its \(n\) momenta of inertia \(B_\alpha\) can be divided into two groups \(B_1 = \dots=B^l\) and \(B_{l+1} =\dots=B^n\), where \(l\) takes the values from 1 to \(n-1\). The case \(n=4\) is considered in details.

MSC:

70E05 Motion of the gyroscope
70K99 Nonlinear dynamics in mechanics

Citations:

JFM 06.0198.01
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