Bicycling geodesics are Kirchhoff rods

Abstract A bicycle path is a pair of trajectories in R n , the ‘front’ and ‘back’ tracks, traced out by endpoints moving line segment fixed length (the ‘bicycle frame’) tangent to back track. Bicycle geodesics are paths whose front track’s critical among all connecting two given placements segment. We write down study associated variational equations, showing that for $n\geqslant 3$?> ⩾ 3 each such geodesic contained 3-dimensional affine subspace tracks these form certain subfamily Kirchhoff rods class curves introduced 1859 Kirchhoff, generalizing planar elastic Bernoulli Euler.