Gaussian Curvature and Gyroscopes

Graham Cox, Mark Levi

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Gyroscope
Total curvature
Gyroscopes
Charge
Magnetic Force
Curved Surface
Magnetic fields
Lagrange
Tangent line
Magnetic Field
Curvature
Motion
Demonstrate
Interpretation

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Gaussian Curvature and Gyroscopes. / Cox, Graham; Levi, Mark.

In: Communications on Pure and Applied Mathematics, Vol. 71, No. 5, 05.2018, p. 938-952.

Research output: Contribution to journalArticle

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