Kana Daniel D., Fox Douglas J.
Southwest Research Institute, San Antonio, Texas 78228.
Chaos. 1995 Mar;5(1):298-310. doi: 10.1063/1.166077.
Complex responses are studied for a spherical pendulum whose support is excited with a translational periodic motion. Governing equations are studied analytically to allow prediction of responses under various excitation conditions. Stability for certain cases of damping is predicted by means of existing analysis and compared with experimental data. Numerical time-step integration of the governing equations is developed to predict responses for various types of excitation and damping conditions. Predicted results are compared with corresponding motions measured in an experimental spherical pendulum system. A data acquisition system is included whereby detailed digitized time histories of the pendulum motion can be established and various parameters can be computed to characterize the type of motion present. Two new vector spaces are defined for describing complex responses which occur for certain specified excitation conditions. It is shown in these parameter spaces that the transition from quasiperiodic to chaotic motions can be carefully quantified in systems with very light damping. This discovery provides a convenient means for comparison of complex motions in the numerical and experimental air pendulum systems. The implications of the results are important for dynamic response in various applications, including fluid motions in satellite tanks and other nonlinear time-dependent physical processes which include very light damping. (c) 1995 American Institute of Physics.
研究了一种球形摆的复杂响应，该摆的支座以平移周期运动激励。对控制方程进行了分析研究，以便预测各种激励条件下的响应。通过现有分析预测了某些阻尼情况下的稳定性，并与实验数据进行了比较。开发了控制方程的数值时间步积分，以预测各种类型的激励和阻尼条件下的响应。将预测结果与在实验球形摆系统中测量的相应运动进行了比较。包含一个数据采集系统，借此可以建立摆运动的详细数字化时间历程，并可以计算各种参数以表征所呈现的运动类型。定义了两个新的向量空间来描述在某些特定激励条件下出现的复杂响应。在这些参数空间中表明，在阻尼非常小的系统中，从准周期运动到混沌运动的转变可以被精确量化。这一发现为比较数值和实验空气摆系统中的复杂运动提供了一种便捷方法。这些结果对于各种应用中的动态响应具有重要意义，包括卫星罐中的流体运动以及其他包含非常小阻尼的非线性时变物理过程。（c）1995美国物理研究所。
