标题： 非笛卡尔思维 显示英文标题

标题： Non-Cartesian Thinking

摘要： 正如我们在基础力学课程中通常教授的那样，选择一个“好的”参考系和方便的坐标轴可能会使问题大大简化。 此外，了解一些守恒量提供了一个极其强大的解决问题的工具。 虽然前一种想法通常在牛顿定律的背景下讨论，但后者则甚至更晚才引入能量守恒。 这项工作展示了在运动学背景下应用上述两种想法的一个优雅例子，从而为后续动力学中使用的标准工具提供了一个“热身”介绍。 参考系的选择（非正交的）和守恒量都相当不寻常，但同时又与当前问题非常直观。 详细讨论了两个这样的问题，并提供了两种不同的方法。 第一种方法甚至不需要微积分的知识。 在附录中，我还介绍了涉及耦合微分方程组的直接求解方法。 此外，在最后还提供了一些练习题和另一个类似的问题供学生“作业”使用。 显示英文摘要

摘要： As we typically teach in an introductory mechanics course, choosing a "good" reference frame with convenient axes may present a major simplification to a problem. Additionally, knowing some conserved quantities provides an extremely powerful problem-solving tool. While the former idea is typically discussed in the context of Newton's Laws, the latter starts with introducing conservation of energy even later. This work presents an elegant example of implementing both aforementioned ideas in the kinematical context, thus providing a "warm-up" introduction to the standard tools used later on in dynamics. Both the choice of the (non-orthogonal) reference frame and the conserved quantities are rather non-standard, yet at the same time quite intuitive to the problem at hand. Two such problems are discussed in detail with two alternative approaches. The first approach does not even require knowledge of calculus. In the appendix, I also present the brute-force solution involving a coupled system of differential equations. In addition, a few exercises and another similar problem for students' "homework" are provided at the end.