The properties of a class of invariant relations of the generalized equations of dynamics

The existence of invariant relations is investigated for the generalized Eu ler-Poisson equations of the dynamics of a rigid body with a fixed point, f or which integrals of energy, angular momentum and the geometric integral e xist. Different formulations are considered, when the potentials of the app lied forces are known and when they are determined according to the form of the invariant relations from the expressions for the first integrals. Earl ier results [1] are extended to the case of one invariant relation of arbit rary structure, and the conditions for invariant relation of layer zero (in P. V Kharlamov's terminology [2]) to exist are considered. (C) 2001 Elsevi er Science Ltd. All rights reserved.