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. 2023 Jul 3;13:10754. doi: 10.1038/s41598-023-36399-4

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© The Author(s) 2023

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(a) A Chaplygin sleigh shaped as a Joukowski foil with a no slip constraint at P in the transverse ( $Y_{b}$ ) direction. The internal reaction wheel is shown by the grey circle. (b) A Joukowski foil with singular distributions of vorticity (red circles corresponding to positive (counterclockwise) vorticity, and blue circles corresponding to negative (clockwise) vorticity) in an otherwise inviscid flow.