A computationally efficient discrete model for low-strain tethers used in many engineering applications is developed without the use of elastic elements. The tether is modelled using N links, with each link treated as a body of revolution where it is assumed the tether spin is negligible to the dynamics, resulting in each link having only two degrees of freedom. A recursive algorithm is developed for the dynamic equations, with the solution procedure being an order N method requiring only a 2 x 2 matrix inversion, resulting in approximately half the computations of the general recursive algorithm. A comparison between the proposed efficient recursive rigid-body model and a lumped point mass model shows that the absence of stiff elastic elements eliminates high-frequency axial vibrations that appear in many lumped point mass tether models. The absence of high-frequency axial vibration facilitates numerical integration of the equations, providing further improvement in computational speed.
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机译：在不使用弹性元件的情况下，开发了用于许多工程应用中的低应变系绳的高效计算离散模型。使用N个链接对系链进行建模，其中每个链接都被视为旋转体，其中假定系链自旋对于动力学可忽略不计，从而导致每个链接仅具有两个自由度。针对动力学方程式开发了一种递归算法，其求解过程是仅需2 x 2矩阵求逆的N阶方法，因此计算量约为普通递归算法的一半。所提出的有效递归刚体模型与集总点模型之间的比较表明，没有刚性弹性元件的存在消除了许多集总点系绳模型中出现的高频轴向振动。高频轴向振动的缺乏促进了方程的数值积分，从而进一步提高了计算速度。
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