Abstract

A class of force evolutionary billiards is discovered that realizes important integrable Hamiltonian systems on all regular isoenergy 3-surfaces simultaneously, i.e., on the phase 4-space. It is proved that the well-known Euler and Lagrange integrable systems are billiard equivalent, although the degrees of their integrals are different (two and one).

中文翻译：

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欧拉和拉格朗日案的力进化台球和台球等价

摘要

发现了一类力进化台球，它同时在所有规则的等能量3面上（即在相4空间上）实现重要的可积哈密顿系统。事实证明，众所周知的Euler和Lagrange可积系统是台球等效的，尽管它们的积分度是不同的（两个和一个）。