107_add_Added Masses of Ship Structures.pdf - 96 3 Added Masses of Three-Dimensional Bodies in Infinite Fluid L2 L 26 = 1 = 220(x)x dx 2T L1(3.6 L2 L 35

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96 3 Added Masses of Three-Dimensional Bodies in Infinite Fluid λ 26 = μ 1 λ = L 2 T L 2 L 1 λ 220 (x)x dx ; (3.6) λ 35 = − μ 1 λ = L B L 2 L 1 λ 330 (x)x dx ; (3.7) λ 55 = μ 1 λ = L B L 2 L 1 λ 330 (x)x 2 dx ; (3.8) λ 66 = μ 1 λ = L 2 T L 2 L 1 λ 220 (x)x 2 dx. (3.9) In the formulas ( 3.1 )–( 3.9 ) the integration is performed between the endpoints of the body whose x -coordinates equal L 1 and L 2 ; μ(λ) and μ 1 (λ) are corrections related to fluid motion along the x -axis; these corrections are different since the motion of fluid along the x -axis is different for cases of linear motion of the body and its rotation. Notice the different sign in the formulas ( 3.6 ) and ( 3.7 ). There is a subtlety related to the choice of correct sign while computing the added masses having the dimension of static moment by the method of plane sections. Consider for example the added mass λ 35 of the body M which is symmetric under the x 1 Oy 1 plane in the coordinate system x 1 y 1 z 1 (Fig. 3.14 ). For the body M (as well as for any other

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• Fall '09
• Geometry, Coordinate system, Polar coordinate system, Coordinate systems

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