Translational and rotational swimming at small Reynolds numbers of a planar assembly of identical spheres immersed in an incompressible viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The translational and rotational swimming velocities of the assembly are deduced from momentum and angular momentum balance equations. The mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocities and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated for prescribed periodic displacements. Explicit calculations are performed for three spheres interacting such that they form ...

中文翻译：

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在具有惯性的不可压缩粘性流体中以小雷诺数游泳

基于单个球体的一组运动方程，研究了浸入不可压缩粘性流体中的相同球体平面组件在小雷诺数下的平移和旋转游泳。球体的运动是由驱动力和源自直接相互作用势的力以及流体作为摩擦和附加质量流体动力相互作用施加的流体动力引起的。从动量和角动量平衡方程推导出组件的平移和旋转游泳速度。一段时间内所需的平均功率由瞬时功率方程计算得出。导出平均游泳速度和平均功率的表达式，对相对平衡位置的位移幅度的二阶有效。因此，可以针对规定的周期性位移评估这些量。对三个相互作用的球体执行显式计算，以便它们形成......