由轨道力驱动的旋转刚体：干摩擦的作用
Spinning rigid bodies driven by orbital forcing: The role of dry friction
摘要：
“圆轨道强迫”使刚体上的一个选定点做圆周运动，而物体绕着该点自由旋转。我们研究这个问题的平面运动的身体受到干摩擦。我们专注于所谓的反向旋转（RR）的效果，其中自旋和轨道旋转是反平行的。类似的反向动力学包括金星和天王星的旋转，轴颈机械轴承，组织生产反应器和手性活性粒子。由于耗散，RR仅可能作为瞬态。这里的瞬态或翻转时间$t_\textrm{f}$取决于循环驱动频率$ω$，与先前研究的粘性情况不同。我们发现$t_\textrm{f}\simω^{γ-1}μ^{-γ/2}$，其中$μ$是摩擦系数和$γ=0$（$γ=2$）低（高）$ω$。RR是否真的发生取决于初始条件以及$μ$和$H$（一个几何参数）。RR变为可能的临界$H_\textrm{c}(μ)$遵循$q$ -指数和$q\simeq1.9$，这是一种比潮湿情况更具限制性的RR情景。我们使用动画来可视化不同的动力学制度，出现从高度非线性耗散机制的干摩擦。我们的结果是有效的，在多个调查的刚体形状。
英文摘要：
A "circular orbital forcing" makes a chosen point on a rigid body follow a circular motion while the body spins freely around that point. We investigate this problem for the planar motion of a body subject to dry friction. We focus on the effect called reverse rotation (RR), where spinning and orbital rotations are antiparallel. Similar reverse dynamics include the rotations of Venus and Uranus, journal machinery bearings, tissue production reactors, and chiral active particles. Due to dissipation, RRs are possible only as a transient. Here the transient or flip time $t_\textrm{f}$ depends on the circular driving frequency $ω$, unlike the viscous case previously studied. We find $t_\textrm{f}\simω^{γ-1}μ^{-γ/2}$, where $μ$ is the friction coefficient and $γ=0$ ($γ=2$) for low (high) $ω$. Whether RRs really occur depends on the initial conditions as well as on $μ$ and $H$, a geometrical parameter. The critical $H_\textrm{c}(μ)$ where RRs become possible follows a $q$-exponential with $q\simeq1.9$, a more restrictive RR scenario than in the wet case. We use animations to visualize the different dynamical regimes that emerge from the highly nonlinear dissipation mechanism of dry friction. Our results are valid across multiple investigated rigid body shapes.
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