基于碰撞响应的三维空间多刚体实时运动仿真

Multi Rigid Bodies Three-Dimensional Real Time Movement Simulation Based on Collision Response

该文将计算机科学与理论力学相结合,以刚性球体为例介绍了多刚体物理运动仿真的步骤和方法。首先论述了单个及多个刚体的运动仿真步骤以及应用叠加原理计算合力及合力矩的方法。然后,针对刚体运动中的不同碰撞响应类型:碰撞接触与临时接触,提出分别建立不同的碰撞响应力学模型,前者采用动量及动量矩定理建立响应模型,后者通过分析刚体的受力和运动状态建立相应的动力学模型。最后,详细讨论了刚性球体的碰撞仿真,包括它的碰撞测定、碰撞响应模型的建立及求解等,实现了三维空间中刚性球体实时、精确、快速的运动仿真,为以后多刚体大规模仿真奠定基础。

This paper combines theoretical mechanics with computer, takes rigid spheres as an example to introduce the step and method of physical movement simulation of multi rigid bodies. First, it states the step and method of movement simulation of the single and multi rigid bodies. Secondly, according to the different type of the collision response of rigid bodies ： collision contacts and temporary contacts, we build different mechanics models. For the former we build response model by momentum and angular momentum theorem; for the latter we build dynamics model by analyzing the mechanics and movement states of rigid body. Lastly, the author discusses the collision simulation of rigid spheres in detail, including the collision determination, building the model of collision response and resolving it and so on. Then we realize the accurate, real - time and quick movement simulation of multi rigid spheres, and build the foundation for the extensive simulation of multi rigid bodies later.