刚体滑移运动中的转捩与奇点
Transitions and singularities during slip motion of rigid bodies
摘要：
由于单边接触运动固体的动力学模型的简单性，通常通过假设刚性、点接触和库仑摩擦来建模。许多作者已经彻底研究了具有沿固定表面在二维中滑动的一个端点的刚性杆（有时称为Painlevé杆）的典型例子。该系统的一般过渡包括三个经典的过渡（滑动粘，滑动反转，提离），以及一个奇异称为动态干扰，即收敛到一个余维2流形的状态空间，其中刚体理论崩溃。本文的目标是确定多点接触的系统中出现的类似奇点，并在更广泛的设置，使初步的步骤对一个全面的清单通用的过渡，从滑移运动到其他类型的动态。我们表明，-除了经典的过渡-动态干扰仍然是一个通用的现象。我们还发现了新形式的奇异性和解决方案的不确定性，以及通用的路线从滑动到自激微观或宏观振荡。
英文摘要：
The dynamics of moving solids with unilateral contacts are often modeled by assuming rigidity, point contacts, and Coulomb friction due to the simplicity of these models. The canonical example of a rigid rod with one endpoint slipping in two dimensions along a fixed surface (sometimes referred to as Painlevé rod) has been investigated thoroughly by many authors. The generic transitions of that system include three classical transitions (slip-stick, slip reversal, lift-off) as well as a singularity called dynamic jamming, i.e. convergence to a codimension 2 manifold in state space, where rigid body theory breaks down. The goal of this paper is to identify similar singularities arising in systems with multiple point contacts, and in a broader setting to make initial steps towards a comprehensive list of generic transitions from slip motion to other types of dynamics. We show that - in addition to the classical transitions - dynamic jamming remains a generic phenomenon. We also find new forms of singularity and solution indeterminacy, as well as generic routes from sliding to self-excited microscopic or macroscopic oscillations.
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