复杂模型中的能量守恒间歇接触运动
Energy-conserving intermittent-contact motion in complex models
AI总结：
本文将无碰撞运动研究从二自由度系统推广到N自由度系统，在谐波近似下由系统频谱确定解，并给出存在条件，最后以带武装躯干双足机器人的摇摆运动为例验证了框架。
摘要：
一些被建模为具有非弹性碰撞的机械系统，却拥有能量守恒的间歇接触解，称为无碰撞解。这种解代表在水平地面上的持续跳跃或行走，对于理解动物运动或设计高效步行机器可能具有重要意义。迄今为止，无碰撞运动仅在简单的二自由度（DOF）系统中，或在谐波近似下解耦为二自由度子系统的系统中得到了解析研究。本文将研究扩展到N自由度系统，将已知解作为一般公式中N=2的特殊情形加以恢复。我们证明，在谐波近似下，无碰撞解由系统的频谱决定。我们给出了一个解存在条件，该条件要求在运动最受约束的阶段至少存在一个振荡简正模态。通过为一个带有武装站立躯干的双足机器人的摇摆运动寻找无碰撞解，说明了所建立的一般框架的应用。
英文摘要：
Some mechanical systems, that are modeled to have inelastic collisions, nonetheless possess energy-conserving intermittent-contact solutions, known as collisionless solutions. Such a solution, representing a persistent hopping or walking across a level ground, may be important for understanding animal locomotion or for designing efficient walking machines. So far, collisionless motion has been analytically studied in simple two degrees of freedom (DOF) systems, or in a system that decouples into 2-DOF subsystems in the harmonic approximation. In this paper we extend the consideration to a N-DOF system, recovering the known solutions as a special N = 2 case of the general formulation. We show that in the harmonic approximation the collisionless solution is determined by the spectrum of the system. We formulate a solution existence condition, which requires the presence of at least one oscillating normal mode in the most constrained phase of the motion. An application of the developed general framework is illustrated by finding a collisionless solution for a rocking motion of a biped with an armed standing torso.
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