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Abstract <p>Investigation of the conditions of conventional stability of steady-state motions of a mechanical system, which assumes existence of an additional partial V.A. Steklov’s integral, has been conducted. Analysis of conventional stability is conducted by Chetayev’s technique with the Lyapunov’s function represented by a full bundle of first integrals of the disturbed motion. It has been ascertained by analytical computations that, in case of a full bundle of integrals, it is possible to formulate sufficient stability conditions, which are the most close to the necessary conditions. It has been demonstrated for the scrutinized system that the boundary conditions of stability may be reached under the limit values of some Langrange multipliers. This allows the researcher to consider the bundles of integrals in the Routh-Lyapunov method and in the Chetayev’s technique differently.</p>

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On Conventional Stability of Steady-State Motions of Mechanical Systems with a Partial Steklov’s Integral

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • M. A. Novikov

摘要

Abstract

Investigation of the conditions of conventional stability of steady-state motions of a mechanical system, which assumes existence of an additional partial V.A. Steklov’s integral, has been conducted. Analysis of conventional stability is conducted by Chetayev’s technique with the Lyapunov’s function represented by a full bundle of first integrals of the disturbed motion. It has been ascertained by analytical computations that, in case of a full bundle of integrals, it is possible to formulate sufficient stability conditions, which are the most close to the necessary conditions. It has been demonstrated for the scrutinized system that the boundary conditions of stability may be reached under the limit values of some Langrange multipliers. This allows the researcher to consider the bundles of integrals in the Routh-Lyapunov method and in the Chetayev’s technique differently.