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 |