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

✍ Scribed by G.V. Gorr; E.M. Mironova

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 628 KB
• Volume: 65
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(01)00046-6

✦ Synopsis

The existence of invariant relations is investigated for the generalized Euler-Poisson equations of the dynamics of a rigid body with a fixed point, for which integrals of energy, angular momentum and the geometric integral exist. Different formulations are considered, when the potentials of the applied forces are known and when they are determined according to the form of the invariant relations from the expressions for the first integrals. Earlier results [l] are extended to the case of one invariant relation of arbitrary structure, and the conditions for invariant relation of layer zero (in f? V Kharlamov's terminology [2]) to exist are considered.