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Table 3 Geometric efficiency for the anormal stroke and different normal strokes with the mechanical cost

From: Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, copepod nauplii and copepod robot

Types of strokes x0(T) l(γ) x0(T)/l(γ)
Simple loops 0.50.10−1 0.994 5.03×10−2
  1.50.10−1 1.86 8.06×10−2
  1.70×10−1 2.02 8.41×10−2
  2.00×10−1 2.28 8.77×10−2
  2.10×10−1 2.50 8.84×10−2
  2.20×10−1 2.47 8.89×10−2
Optimal stroke 2.23×10 −1 2.56 8.90×10 −2
Fig. 14 (bottom)    
  2.30×10−1 2.59 8.90×10−2
  2.50×10−1 2.85 8.76×10−2
  2.60×10−1 3.04 8.54×10−2
Abnormal 2.742×10−1 4.93 5.56×10−2
Limaçon 2.500×10−1 3.35 7.46×10−2
  1. Bold represents the most efficient stroke