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中文摘要：
以三质点弹性碰撞系统为例，考虑质点之间相互作用时局部的接触变形信息，并基于矩阵函数理论得到了三质点弹性碰撞系统Hamilton空间中的严格理论解。基于理论分析结果，详细讨论了不同质点之间的质量比以及接触刚度比对质点碰撞后的动力学行为的影响，包括可能产生的不同分离模式，接触点的分离次序，以及由此可能导致的内碰撞现象等。
英文摘要：
Multiple impact and multiple contact problems are difficult, while using rigid dynamic theory. The rigid-solution may not be unique in some cases. The stiffness ratio and elastic vibration between different bodies can greatly influence the post-velocities of each body. In this paper, an effective theoretical method based on Hamilton space is developed to analyze the 3-ball system with multiple impact. By using the linear springs to model the compliance at each contact point, the strict theoretical solutions are obtained for this problem. The effects of various parameters, such as the mass ratio and stiffness ratio, on the separation behavior of each ball are carefully studied. The rigid-body solutions are some sort of limits of the theoretical results given in this paper. Meanwhile, the phenomena of internal impact between balls are revealed and the parametric area on α-γ plane is determined through analyzing the theoretical results.
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