Gaussian Curvature and Gyroscopes

Graham Cox, Mark Levi

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)938-952
Number of pages15
JournalCommunications on Pure and Applied Mathematics
Volume71
Issue number5
DOIs
StatePublished - May 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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