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

It is pointed out that the current form of the 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 this fact...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2016-12, Vol.76 (12), p.1-4, Article 655
Main Authors: Hu, L. D., Lian, D. K., Liu, Q. H.
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Centripetal force
Elementary Particles
Equations of motion
Geodesy
Hadrons
Heavy Ions
Hyperspaces
Letter
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
String Theory
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Summary:It is pointed out that the current form of the 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 this fact is taken into consideration, the equation takes the same form as that for the 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 preferable.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-016-4473-2