标题： 太空海盗：涉及延迟时间的追逐曲线问题 显示英文标题

标题： Space pirates: a pursuit curve problem involving retarded time

摘要： 我们重新审视了18世纪皮埃尔·布格在解决的经典的追击曲线问题，考虑到信息以有限速度传播。在某种程度上，这可以被视为对该问题的相对论修正，尽管在推导或理解其解时并不需要爱因斯坦的相对论理论。对这个广义追击问题的讨论为引入滞后时间的概念提供了绝佳的机会，而无需涉及电磁辐射研究中固有的复杂性（通常在此处首次见到该概念），这使该问题具有明确的教学动机。我们找到了描述该问题的微分方程，对其进行数值求解，将解与布格的解在不同参数值下进行比较，并推导出追击者捕捉被追击者的必要且充分条件，补充了霍恩塞尔尔斯之前的工作。 显示英文摘要

摘要： We revisit the classical pursuit curve problem solved by Pierre Bouguer in the 18th century, taking into account that information propagates at a finite speed. To a certain extent, this could be seen as a relativistic correction to that problem, though one does not need Einstein's theory of relativity in order to derive or understand its solution. The discussion of this generalized problem of pursuit constitutes an excellent opportunity to introduce the concept of retarded time without the complications inherent to the study of electromagnetic radiation (where it is usually seen for the first time), which endows the problem with a clear pedagogical motivation. We find the differential equation which describes the problem, solve it numerically, compare the solution to Bouguer's for different values of the parameters, and deduce a necessary and sufficient condition for the pursuer to catch the pursued, complementing previous work by Hoenselaers.