论文标题
自行车路径，弹性和亚摩恩尼亚几何形状
Bicycle paths, elasticae and sub-Riemannian geometry
论文作者
论文摘要
我们将平面僵化运动群的次摩nanian几何形状与“骑自行车的数学”联系起来。我们表明，这种几何的大地测量学对应于自行车路径，其前轨是非反射的Euler弹性或直线，并且其无限的无限型地球学（或“度量线”）对应于自行车路径，其前线是直线或``Euler's Solitons''（也称为euler's Solitons'（也称为Syntractrix syntractrix syttrixs'Curves）。
We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight lines, and that its infinite minimizing geodesics (or `metric lines') correspond to bike paths whose front tracks are either straight lines or `Euler's solitons' (also known as Syntractrix or Convicts' curves).
