FIRST INTEGRALS OF THE EQUATIONS OF MOTION FOR THE GENERALIZED GYROSCOPE IN R~n

摘要

By analogy with three-dimensional space, the generalized gyroscope is a rigid body with a fixed point whose moments of inertia relative to n hyperplanes can be divided into two groups such that the moments belonging to each group are equal. In this case, the well-known system of n(n - 1)/2 generalized dynamic Euler equations has a certain number of first integrals and can be reduced to a linear nonhomogeneous nonautonomous system. The number of first integrals depends on the inertial structure of the gyroscope. The case when n = 4 is studied in detail.