论文标题
关于Joachimsthal Intemall和Poritsky Property的评论
Remarks on Joachimsthal integral and Poritsky property
论文作者
论文摘要
椭圆形的台球在Joachimsthal的积分中具有积分线性。我们表明，这种整体的存在是锥体的特征。我们将此结果扩展到球形和双曲线几何形状以及更高的维度。我们将Joachimsthal积分的存在与Poritsky Property（台球曲线的属性）联系起来，在H. Poritsky之后被称为So So So，其重要的1950年论文是对台球问题的早期研究之一。
The billiard in an ellipse has an integral linear in momentum, the Joachimsthal integral. We show that the existence of such an integral characterizes conics. We extend this result to the spherical and hyperbolic geometries and to higher dimensions. We connect the existence of Joachimsthal integral with the Poritsky property, a property of billiard curves, called so after H. Poritsky whose important 1950 paper was one of the early studies of the billiard problem.
