The swimming of a deformable uniform sphere is studied in second order perturbation theory in the amplitude of the stroke. The effect of the first order reaction force on the first order center of mass velocity is calculated in linear response theory by use of Newton’s equation of motion. The response is characterized by a dipolar admittance, which is shown to be proportional to the translational admittance. As a consequence the mean swimming velocity, calculated in second order perturbation theory, depends on the added mass of the sphere. The mean swimming velocity and the mean rate of dissipation are calculated for several selected strokes.

中文翻译：

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用惯性在粘性不可压缩流体中游动均匀变形球

在二阶微扰理论中研究了可变形均匀球体在行程幅度上的游动。利用牛顿运动方程，在线性响应理论中计算了一级反作用力对一级质量中心的影响。响应的特征在于偶极导纳，该极偶极导纳与平移导纳成正比。结果，以二阶微扰理论计算的平均游泳速度取决于球体的附加质量。计算了几个选定行程的平均游泳速度和平均耗散率。