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# 2005reading6 - 2.016 Hydrodynamics Reading#6 2.016...

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2.016 Hydrodynamics Reading #6 Looking simply at a body in two-dimensions we can have linear motion in two directions and rotational motion in one direction. (Think of these coordinates as if you were looking down on a ship.) Two dimensional motion with axis (x,y) fixed on the body. 1: Surge, 2: Sway, 6: Yaw The unsteady forces on the body in the three directions are: = m 11 du 1 + m du 2 + m du 6 (6.6) F 1 12 dt 16 dt dt F 2 = m 21 du 1 + m du 2 + m du 6 (6.7) dt 22 dt 26 dt F 6 = m 61 du 1 + m du 2 + m du 6 (6.8) dt 62 dt 66 dt Where F 1 , F 2 , and F 6 , are the surge (x-) force, sway (y-) force and yaw moments respectively. It is common practice in Ocean Engineering and Naval Architecture to write the moments for roll, pitch, and yaw as F 4 , F 5 , and F 6 and the angular motions in these directions as X 4 , X 5 , and X 6. This set of equations, (6.6)-(6.8), can be written in matrix form, F = [ ] ± , M u du 1 dt m 11 m 12 m 16 ⎤⎜ F = m 21 m 22 m 26 du 2 (6.9) dt m 61 m 62 m 66 ⎥⎜ du 6 dt version 3.0 updated 8/30/2005 -2- © 2005 A. Techet
2.016 Hydrodynamics Reading #6 Considering all six degrees of freedom the Force Matrix is: ± u 1 m 11 m 12 m 13 m 14 m 15 m 16 ⎤⎛ ⎥⎜ ± u 2 m m 21 m 22 m 23 m 24 m 25 m 26 ⎥⎜ 36 ⎥⎜ ± m 31 m 32 m 33 m

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