Open AccessStability of equilibrium state of a kind of nonlinear relative rotation dynamic system and associated harmonic approximate solution
Author(s) -
Meng Zong,
Bin Liu
Publication year - 2008
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.57.1329
Subject(s) - nonlinear system , perturbation (astronomy) , lyapunov function , rotation (mathematics) , physics , harmonic , stability (learning theory) , classical mechanics , mathematical analysis , mathematics , computer science , quantum mechanics , geometry , machine learning
The nonlinear dynamic equation with two masses in relative rotation is established, which contains a kind of generalized nonlinear elastic force. Using variable gradient method, the Lyapunov function is gotten, and the stability of the relative rotation nonlinear autonomous system is studied. The approximate solution of the associated harmonic response of the relative rotation nonlinear non-autonomous system under two forcing excitations of different frequencies is obtained by the method of perturbation.