李戈, 时志高, 谢奇之, 刘江河, 卜振翔. 基于Mathematica对保守双摆的研究[J]. 南昌航空大学学报(自然科学版), 2016, 30(3): 40-43,71. DOI: 10.3969/j.issn.1001-4926.2016.03.008
引用本文: 李戈, 时志高, 谢奇之, 刘江河, 卜振翔. 基于Mathematica对保守双摆的研究[J]. 南昌航空大学学报(自然科学版), 2016, 30(3): 40-43,71. DOI: 10.3969/j.issn.1001-4926.2016.03.008
LI Ge, SHI Zhi-gao, XIE Qi-zhi, LIU Jiang-he, BU Zhen-xiang. The Research of the Conservative Double Pendulum by using Mathematica[J]. Journal of nanchang hangkong university(Natural science edition), 2016, 30(3): 40-43,71. DOI: 10.3969/j.issn.1001-4926.2016.03.008
Citation: LI Ge, SHI Zhi-gao, XIE Qi-zhi, LIU Jiang-he, BU Zhen-xiang. The Research of the Conservative Double Pendulum by using Mathematica[J]. Journal of nanchang hangkong university(Natural science edition), 2016, 30(3): 40-43,71. DOI: 10.3969/j.issn.1001-4926.2016.03.008

基于Mathematica对保守双摆的研究

The Research of the Conservative Double Pendulum by using Mathematica

  • 摘要: 根据Lagrange方法,建立了保守双摆系统的数学模型,利用Mathematica分别计算了保守双摆系统在高能量和低能量时广义坐标的数值解,并提出了验证该数值解的可靠性的方法。然后编写了交互式的全参数混合控件,当系统在较高能量下,利用控件对初值进行扰动,找到了由拟周期运动演变为混沌运动的临界初值。仿真结果显示该交互式控件可为涉及到双摆机构及现代多体动力学中的混沌内容提供新方案。

     

    Abstract: According to Lagrange method, a conservative double pendulum mathematical model was conceived.The solution of the generalized coordinates of the conservative double system was respectively obtained, where it was in high energy or low energy by using mathematical. Then, a method was come up with to demonstrate the reliability of the solution. After that, an interactive full parameter hybrid control was fabricated. By using the control disturbed the initial value, a critical value at which the motion of the quasi periodic motion transformed into a chaotic motion was obtained where the conservative double pendulum system was in high energy. The simulation results provide some new schemes for the contents of chaos of the double mechanism and the modern multibody dynamics.

     

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