Abstract The evolution of a system of mutually gravitating particles is considered taking into account the energy loss in collisions. Collisions can be described in various ways. One can use the theory of inelastic impact of solids with Newton’s recovery coefficient for the relative velocity of bouncing particles. In numerical implementation, the main difficulty of this approach is to track and refine the huge number of time moments of particle collisions. Another approach is to supplement the gravitational potential with the potential of repulsive forces similar to the Lennard-Jones intermolecular forces. Numerical experiments show that, under the Jacobi stability condition, both models lead to a qualitatively identical evolution with the formation of stable configurations. For an infinite number of particles, the probability density function is determined by the system of Vlasov–Boltzmann–Poisson equations. Our proposed methodology corresponds to the use of the Vlasov kinetic equation with a potential of the Lennard-Jones type.

中文翻译：

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具有修正势的多体系统的雅可比稳定性

摘要 考虑到碰撞中的能量损失，考虑了相互引力粒子系统的演化。碰撞可以用多种方式描述。人们可以使用固体的非弹性冲击理论和牛顿恢复系数来计算弹跳粒子的相对速度。在数值实现中，这种方法的主要困难是跟踪和细化粒子碰撞的大量时间矩。另一种方法是用类似于 Lennard-Jones 分子间力的排斥力的潜力来补充引力势。数值实验表明，在雅可比稳定条件下，两种模型都导致了质量相同的演化，并形成了稳定的构型。对于无限数量的粒子，概率密度函数由 Vlasov-Boltzmann-Poisson 方程组确定。我们提出的方法对应于使用具有 Lennard-Jones 类型潜力的 Vlasov 动力学方程。