中文摘要：

建立了动态描述海底电缆铺设过程中电缆运动轨迹的微分方程模型,同时提出了静态解的存在条件和相应的数值算法.在实际电缆铺设过程中可用来合理设计探测船航行速度和路线以保证电缆可以沉放到设定的位置.

英文摘要：

In this paper,we establish a differential model to describe the installation process of undersea cable.At the same time,we put forward a numerical method to solve the mathematical model approximately and prove the existence of solution of the mathematical model in a special case.In practice,we can use the results in this paper to design the proper route of the messenger spacecraft to guarantee that the cable drop to the design position.