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| On the Chaotic Dynamic Behaviour of the Rigid Rod-Spring Pendulum Model |
| ZHAO Cong, YU Hongjie
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| Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200240, China |
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Abstract A planar rigid rod-spring pendulum model was constructed and dimensionless dynamic equation 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 dynamic equation is strongly nonlinear as the fast and slow variables couple each other. A cubic interpolation 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 conditions. It is also found that the fast variable may transform to chaos via the quasi-periodic torus breakdown.
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Received: 16 September 2014
Published: 25 February 2025
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