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Table 2 Geometric efficiency for the abnormal stroke and different normal strokes with the Euclidean cost

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

Types of stroke x0(T) l(γ) x0(T)/l(γ)
Simple loops 5.50×10−2 1.98 2.52×10−2
  1.40×10−1 3.79 3.70×10−2
  1.70×10−1 4.34 3.92×10−2
  2.00×10−1 4.95 4.04×10−2
  2.10×10−1 5.11 4.11×10−2
Optimal stroke 2.17×10 −1 5.18 4.19×10 −2
Fig. 14 (top)    
  2.20×10−1 5.35 4.11×10−2
  2.30×10−1 5.62 4.09×10−2
  2.50×10−1 6.31 3.97×10−2
  2.74×10−1 9.05 3.03×10−2
Abnormal 2.74×10−1 10.7 2.56×10−2
Limaçon 2.00×10−1 6.15 3.25×10−2
  1. Bold represents the most efficient stroke