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CONTROLLABILITY OF A PAIR OF SWIMMING MICROROTORS IN A BOUNDED DOMAIN AT LOW REYNOLDS NUMBER

机译:在低雷诺数的有界域中的一对游泳微流器的可控性

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We investigate the dynamics of a pair of spinning spheres or microrotors in a fluid at low Reynolds numbers. These microro-tors are each approximated by a rotlet, a fundamental singularity of the Stokes equation. Singularities of Stokes flows serve as useful theoretical models for microswimmers and micro-robots. Rot-let models of microswimmers have received less attention since a rotlet cannot generate translation by itself if the only control input is the rate of spin or strength of the rotlet. However a pair of rotlets can interact and execute net motion. In an unbounded domain of fluid, the positions of a pair of rotlets are not fully controllable due to the existence of an invariant. However, in a confined domain, we show that the positions of the pair of spheres are small time locally controllable. We show how control inputs can be constructed based on combinations of Lie brackets to move the rotlets from one point to another in the domain.
机译:我们在低雷诺数的流体中调查一对纺丝球或微运动器的动态。这些微型缩小件均由罗特近似,斯托克斯方程的基本奇异性。斯托克斯流量的奇点为微大机器人和微机器人用作有用的理论模型。由于唯一的控制输入是旋转速率或圆形速度的速度,因此腐烂的微威尔人的模型感应不太关注。然而,一对罗let可以交互和执行净运动。在不受约束的流体领域中,由于不变的存在,一对棘轮的位置不完全可控。然而,在一个限制的域中,我们表明一对球体的位置很小是局部可控的。我们展示了如何基于Lie括号的组合构建控制输入,以将旋转从一个点移动到域中的另一个点。

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