| Kirchhoff相似性原理与弹性纤体的空间混沌构形 |
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| 引用本文： | 梁以德,匡金炉. Kirchhoff相似性原理与弹性纤体的空间混沌构形[J]. 华南理工大学学报(自然科学版), 2003, 31(Z1): 1-6 |
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| 作者姓名： | 梁以德 匡金炉 |
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| 作者单位： | 香港城市大学建筑系,香港 |
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| 基金项目： | 香港城市大学校科研和教改项目 |
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| 摘 要： | 着重讨论三维弹性纤体空间静态构形力学与陀螺体的时间动态力学之间的广义Kirchhoff相似性原理.通过研究陀螺体的受扰姿态运动的哈密顿结构及与其相关的Melnikov积分,解析地确定了弹性纤体静态混沌构形可能产生的条件.采用7～8阶Runge-Kutta算法定量地核对了由Melnikov方法所得的定性结果.三维弹性纤体存在于不同尺度的物质结构中(从微观的DNA双螺旋结构到宏观的弹性细杆、细绳、电缆、音像磁带和卫星系绳等).仿真结果表明,在合适的载荷条件下,弹性纤体的平衡构形将呈现起因于同宿/异宿分叉的混沌.
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| 关 键 词： | 弹性纤体 混沌 同宿/异宿分叉 Melnikov积分 |
Kirchhoff Analogy and Spatially Chaotic Configuration of Buckled Elastica |
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| Abstract. Kirchhoff Analogy and Spatially Chaotic Configuration of Buckled Elastica[J]. Journal of South China University of Technology(Natural Science Edition), 2003, 31(Z1): 1-6 |
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| Authors: | Abstract |
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| Abstract: | The aim of this paper is to discuss the extended Kirchhoff analogy between the spatial equilibriumof a 3D force-free buckled elastica and the temporal dynamics of the torque-free gyrostat. In conjunction withthe Melnikov integral, we shall determine analytically the conditions for the possible onset of spatial chaos inthe elastica by exploring the Hamiltonian structure of the rotational motion of a perturbed gyrostat. The qualita-tive results are quantitatively cross-checked by the 7 ～ 8th order Runge-Kutta algorithm. The elastica appears atdifferent scales from microscopic chains of super coiling DNA structures to macroscopic rods/ropes/cables/sa-tellite tethers. The simulation results show that there exists homoclinic/heteroclinic bifurcations to chaos in theequilibrium of the elastica under the appropriate load conditions, equivalently, boundary conditions. |
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| Keywords: | buckled elastica chaos homoclinic/heteroclinic bifurcations Melnikov's integral |
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