一种刚性杆-弹簧摆模型的混沌动力学行为研究

针对具有大范围运动慢变量和小幅度振荡快变量的强非线性刚-柔耦合多体系统,建立一种刚性杆-弹簧摆模型。给出了该双时间尺度变量系统的无量纲动力学方程,以频率比、摆长比作为控制参数,对系统在不同初始条件下的非线性动力学行为进行了数值模拟和分析。由于快、慢变量之间的相互耦合,动力学方程表现出强非线性的特点,对数值方法提出了更高要求。采用一种高精度的三次Lagrange插值精细积分法进行数值求解,并给出了系统不同的运动状态对应的参数范围。数值分析结果表明,系统变量在不同的控制参数和初始条件下,呈现出了复杂的混沌动力学行为,快变量显示了经由准周期环面破裂分岔通往混沌的途径。

On the Chaotic Dynamic Behaviour of the Rigid Rod-Spring Pendulum Model

A planar rigid rod‐spring pendulum model was constructed and dimensionless dynamic e‐quation was given .We numerically simulated and analyzed the dynamical behavior of the two‐time‐scale system while the frequency ratio and length ratio and initial conditions vary .The dy‐namic equation is strongly nonlinear as the fast and slow variables couple each other .A cubic in‐terpolation precise integration method was applied to solve nonlinear dynamic equation .We also employ the Poincaré maps and the maximum Lyapunov exponent methods .Numerical simulation results demonstrate that the system presents complex chaotic motion in different parameters con‐ditions .It is also found that the fast variable may transform to chaos via the quasi‐periodic torus breakdow n .