### 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 language | English (US) |
---|---|

Pages (from-to) | 938-952 |

Number of pages | 15 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 71 |

Issue number | 5 |

DOIs | |

State | Published - May 2018 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*71*(5), 938-952. https://doi.org/10.1002/cpa.21731

}

*Communications on Pure and Applied Mathematics*, vol. 71, no. 5, pp. 938-952. https://doi.org/10.1002/cpa.21731

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Gaussian Curvature and Gyroscopes

AU - Cox, Graham

AU - Levi, Mark

PY - 2018/5

Y1 - 2018/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85038246167&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85038246167&partnerID=8YFLogxK

U2 - 10.1002/cpa.21731

DO - 10.1002/cpa.21731

M3 - Article

AN - SCOPUS:85038246167

VL - 71

SP - 938

EP - 952

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -