摘要
对受周期外力驱动的对称双弹簧振子进行了研究,建立了系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法,求解非线性方程和判断解的性质.通过改变系统参数,画出时域图、相图及分岔图等.计算分析和数值实验发现,这个简单的力学系统存在十分丰富的动力学行为(分岔、混沌).理论分析和数值实验结果一致.
The model of forced and damped transverse oscillation of a symmetric double-spring oscillator is designed and its dynamical equation is proposed. By using the method of linear stability analysis, the stability of the system is discussed in the neighborhood of the equilibrium point. The character of the solution can be obtained by numerical simulation and other analysis methods. Time-series diagram, phase diagram and bifurcation diagram for the oscillation of this system are plotted. These results show that there are various kinds of dynamical phenomena. Theoretical analysis is in agreement with numerical simulation.
出处
《大学物理》
北大核心
2008年第10期18-21,29,共5页
College Physics
基金
廊坊师范学院科学研究资助项目(LSAQ200701)
廊坊市科技局科研基金资助项目(2007050204)
