曲面上质点的向心力定律和运动方程
The centripetal force law and the equation of motion for a particle on a curved hypersurface
摘要：
本文指出，目前的约束在超曲面上的质点的外在运动方程形式，实际上是一个半成品，因为它是在没有考虑质点永远不能离开曲面上的测地线的情况下建立的。一旦考虑到这一事实，方程的形式与向心力定律的形式相同，只要重新解释符号，使定律适用于更高的维度。讨论了如何构造这些方程的算符形式的问题，研究表明基于外生运动方程的约束系统量子化是有利的。
英文摘要：
It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once the fact be taken into consideration, the equation takes that same form as that for centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is favorable.
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