Algorithm for the derivation of Liapunov's function in the form of a sum of squares of integrals: PMM vol. 42, no. 5, 1978 pp. 946–949

Abstract

Conditions of motion stability of a system admitting first integrals are obtained in the form of sufficient conditions of zero solution uniqueness of a nonlinear system. The problem of stability of permanent rotations of a heavy solid body with a single fixed point is illustrated here by the establishment of three sufficient conditions of such stability. Two of these coincide with those derived earlier [1], while the third is more general. The proposed procedure for the derivation of Liapunov's function from integrals of motion is a synthesis of a number of known methods [2–4]. The problem used here as an illustration was considered by several authors (see e.g., [5–9]). A new set of permanent rotations is formulated directly on the admissible arc on the Staude cone in conformity with Rumiantsev's theories.