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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。
This paper focuses on the generalized Kirchhoff similarity principle between the static configuration mechanics of three-dimensional elastic body and the time dynamics of gyroscope. By investigating the Hamiltonian structure perturbed by the gyroscope and the Melnikov integrals associated with it, the possible conditions of the static chaos configuration of the elastic fiber are analytically determined. The qualitative results obtained by the Melnikov method are quantitatively verified by the 7-8 Runge-Kutta algorithm. Three-dimensional elastic fibers exist in different scales of material structure (microscopic DNA double helix structure to macroscopic elastic rod, string, cable, audio tape and satellite tether, etc.). The simulation results show that under suitable loading conditions, the equilibrium configuration of the elastic filament will exhibit chaos resulting from bifurcation of homoclinic / heteroclinic.