A well-known problem in classical mechanics that is often presented for pedagogical purposes involves a small mass that slides without friction under a gravitational force on the surface of a sphere. Commonly, students are asked to find the angular position where a mass with no azimuthal motion leaves the spherical surface, and this question is easily within the reach of most intermediate physics students. However, a complete solution for more general motion of the mass on the spherical surface (including friction) may be suitable for many advanced undergraduates. Without friction, the problem including azimuthal motion is really an inverted version of an ideal spherical pendulum. This problem is also useful for extending discussion in classical mechanics to more sophisticated topics beyond solving Newton's laws of motion, such as the importance of conservation laws and constants of motion as they relate to symmetry, conservative versus dissipative forces, and the role of constraints.

中文翻译：

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分析质量在具有摩擦力的球体上滑动的运动

经典力学中一个众所周知的问题，通常用于教学目的，涉及一个小质量，它在球体表面的重力作用下无摩擦地滑动。通常，学生会被要求找到一个没有方位角运动的质量离开球面的角位置，这个问题很容易在大多数中级物理学生的范围内完成。然而，对于质量在球面上的更一般运动（包括摩擦）的完整解决方案可能适用于许多高级本科生。没有摩擦，包括方位角运动在内的问题实际上是理想球摆的倒置版本。这个问题对于将经典力学中的讨论扩展到更复杂的主题也很有用，而不是解决牛顿运动定律，