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 |