Abstract Mathematical modelling of “space debris” is one of the priority areas in ensuring the safety of space flights. We consider interaction of the dust particle clouds in accordance with our mathematical model of this phenomenon. The evolution of an ensemble of gravitating particles is studied, taking into account possible contact interactions, during which energy dissipation can occur. We consider collisions in frame of Newton theory of rigid impact, and another way, we introduce an additional potential of repulsive forces similar to the Lennard-Jones intermolecular forces. Computer experiments show that as a result of evolution the stable compact clusters can be formed.

中文翻译：

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致密空间碎片云的相互作用

摘要 “空间碎片”的数学建模是保障空间飞行安全的重点领域之一。我们根据我们对这种现象的数学模型来考虑尘埃粒子云的相互作用。研究了引力粒子系综的演化，同时考虑了可能发生的接触相互作用，在此期间可能发生能量耗散。我们在牛顿刚性碰撞理论的框架中考虑碰撞，另一种方式，我们引入了类似于伦纳德 - 琼斯分子间力的排斥力的额外潜力。计算机实验表明，作为演化的结果，可以形成稳定的致密星团。