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A numerical method for the optimum motion of an undulatory swimming plate is presented. The optimum problem is stated as minimizing
the power input under the condition of fixed thrust. The problem is singular for the invisible modes, and therefore the commonly
used Lagrange multiplier method cannot predict an optimum solution but just a saddle point. To eliminate the singularity,
an additional amplitude inequality constraint is added to the problem. A numerical optimization code with a sequential quadratic
programming method is used to solve the problem. The method is applied to several cases of the motion of two-dimensional and
three-dimensional undulatory plates, and the optimum results are obtained. 相似文献
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