相对转动非线性动力系统的稳定性与强迫激励下的近似解

Stability of nonlinear dynamical system of relative rotation and approximate solution under forced excitation

研究相对转动非线性动力系统的运动稳定性.建立具有一般广义阻尼力和外扰激励的一类两质量相对转动非线性动力系统的动力学方程.研究相对转动非线性动力自治系统的稳定性,证明系统在一定条件下可发生闭轨分岔.应用多尺度法得到强迫激励下非自治系统的近似解.

The stability of nonlinear dynamical system of relative rotation is studied. Firstly, the dynamics equation of relative rotation autonomous nonlinear dynamical system with commonly damped force and forced excitation is deduced. Secondly, the stability of relative rotation nonlinear dynamical system is studied. For the nonlinear dynamical system, it is proved that the closed orbit bifurcation can occur under some conditions. Finally, The approximate solution of the equation under forced excitation is obtained by the method of multiple scales.