期刊
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
卷 71, 期 5, 页码 938-952出版社
WILEY
DOI: 10.1002/cpa.21731
关键词
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资金
- National Science Foundation [DMS-1412542]
- NSERC [RGPIN-2017-04259]
We relate Gaussian curvature to the gyroscopic force, thus giving a mechanical interpretation of the former and a geometrical interpretation of the latter. We do so by considering the motion of a spinning disk constrained to be tangent to a curved surface. It is shown that the spin gives rise to a force on the disk that is equal to the magnetic force on a point charge moving in a magnetic field normal to the surface, of magnitude equal to the Gaussian curvature, and of charge equal to the disk's axial spin. In a special case, this demonstrates that the precession of Lagrange's top is due to the curvature of a sphere determined by the parameters of the top. (c) 2017 Wiley Periodicals, Inc.
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