论文标题
骑自行车的测量学是Kirchhoff Rods
Bicycling geodesics are Kirchhoff rods
论文作者
论文摘要
自行车路径是$ {\ mathbb r}^n $，“前”和“后”轨道中的一对轨迹，被固定长度的移动线段（“自行车框架”）的端点所追踪，并切入后轨道。自行车大地管是自行车路径，其前轨的长度在连接两个给定的线段放置位置的所有自行车路径中至关重要。 我们写下并研究了相关的变异方程，表明，对于$ n \ geq 3 $，每个地理上的地理都包含在一个3维的仿射子空间中，并且这些地理学的前轨构成了Kirchhoff Rods的某些亚家族，这是G. Kirchhoff在1859年引入的一类曲线。
A bicycle path is a pair of trajectories in ${\mathbb R}^n$, the `front' and `back' tracks, traced out by the endpoints of a moving line segment of fixed length (the `bicycle frame') and tangent to the back track. Bicycle geodesics are bicycle paths whose front track's length is critical among all bicycle paths connecting two given placements of the line segment. We write down and study the associated variational equations, showing that for $n\geq 3$ each such geodesic is contained in a 3-dimensional affine subspace and that the front tracks of these geodesics form a certain subfamily of Kirchhoff rods, a class of curves introduced in 1859 by G. Kirchhoff, generalizing the planar elastic curves of J. Bernoulli and L. Euler.
