2016/07/12 by Graham Cox, Cox, Graham, Mark Levi +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.DG #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.1607.03217
12 pages, 10 figures; v2: minor changes to notation and exposition, Section 2.3 and Figure 4 added
arxiv created 2017/04/26 · arxiv updated 2017/04/27
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 which 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.