The centripetal force law and the equation of motion for a particle on a curved hypersurface

Abstract

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.

arXiv comment5 pages, major revision

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• No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution
• Spin Force and Torque in Non-relativistic Dirac Oscillator on a Sphere
• Geometric momentum and angular momentum for charge-monopole system
• The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere