论文标题
投影动力和可集成的玻尔兹曼台球模型
Projective Dynamics and an Integrable Boltzmann Billiard Model
论文作者
论文摘要
本说明的目的是解释由Gallavotti和Jauslin在Arxiv中建立的可集成Boltzmann台球模型的整合性：或者通过投影动力学的观点或雅克斯林在Arxiv：2008.01955中建立。额外的第一个积分被证明与半球相应系统的能量有关。我们表明，该观点也适用于通过开普勒 - 库仑问题定义的飞机中的某些其他台球模型。该方法还导致通过球形开普勒 - 库仑问题定义的球体上的一个综合台球模型家族。
The aim of this note is to explain the integrability of an integrable Boltzmann billiard model, previously established by Gallavotti and Jauslin in arXiv:2008.01955, alternatively via the viewpoint of projective dynamics. The additional first integral is shown to be related to the energy of a corresponding system on a hemisphere. We show that this viewpoint applies to certain other billiard models in the plane defined through Kepler-Coulomb problems as well. The approach also leads to a family of integrable billiard models on the sphere defined through the spherical Kepler-Coulomb problem.
