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Energy dissipation and behavioral regimes in an autonomous double pendulum subjected to viscous and dry friction damping
European Journal of Physics ( IF 0.7 ) Pub Date : 2021-07-19 , DOI: 10.1088/1361-6404/ac05d2
Kishan R Sawant 1 , V Shrikanth 2
Affiliation  

The nonlinear dynamics of a system of a compound double pendulum are experimentally analyzed and numerically verified. The experiments are carried out for a combination of initial angles in the range 0 ⩽ θ 0, ϕ 0 ⩽ 180, with zero initial angular velocity and with an increment of 1. The motion of the pendula is captured in the video and the individual pendula are tracked using image processing. The energy dissipation in the system is evaluated using the Rayleigh dissipation function to include non-conservative forces as well, as a lumped parameter in the Lagrangian equation. Furthermore, the experimental and the numerical results are brought to agreement by tuning the dissipation factors. The linear, nonlinear and chaotic behavior of the system is classified in the coordinate plane. The behavioral regime represents the dependency of the nature of the system on the total energy and the difference in instantaneous amplitudes of the pendula. Uncertainty in the behavior of the system is observed in the transition region from the nonlinear to the chaotic regime due to the sensitivity of the system to the initial conditions. The dependence of the dissipation factors on the angular displacements is represented as a surface plot, which highlights the dominance of viscosity in the higher amplitude oscillations and the dominance of dry friction in the lower amplitude oscillations. This phenomenon is established by observing the nature of decay in the response plots of the pendula.



中文翻译:

受粘性和干摩擦阻尼作用的自主双摆中的能量耗散和行为机制

对复合双摆系统的非线性动力学进行了实验分析和数值验证。实验是针对 0 ⩽ θ 0 , ϕ 0范围内的初始角度的组合进行的⩽ 180,初始角速度为零,增量为 1。在视频中捕获钟摆的运动,并使用图像处理跟踪单个钟摆。系统中的能量耗散使用瑞利耗散函数进行评估,以包括非保守力,作为拉格朗日方程中的集总参数。此外,通过调整耗散因子使实验和数值结果一致。系统的线性、非线性和混沌行为在坐标平面内分类。行为状态代表系统性质对总能量和钟摆瞬时振幅差异的依赖性。由于系统对初始条件的敏感性,在从非线性状态到混沌状态的过渡区域中观察到系统行为的不确定性。耗散因子对角位移的依赖性表示为表面图,它突出了粘度在较高振幅振荡中的主导地位和干摩擦在较低振幅振荡中的主导地位。这种现象是通过观察钟摆响应图中衰减的性质而建立的。这突出了粘度在较高振幅振荡中的主导地位和干摩擦在较低振幅振荡中的主导地位。这种现象是通过观察钟摆响应图中衰减的性质而建立的。这突出了粘度在较高振幅振荡中的主导地位和干摩擦在较低振幅振荡中的主导地位。这种现象是通过观察钟摆响应图中衰减的性质而建立的。

更新日期:2021-07-19
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