r11_heavepitch - 13.42 Spring 2005 13.42 Design Principles...

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13.42 Spring 2005 13.42 Design Principles for Ocean Vehicles Prof. A.H. Techet Spring 2005 1. Coupled Equation of Motion in Heave and Pitch x 3 x 5 Once we have set up the simple equation of motion for a vessel in heave it is natural to extend this discussion to the coupled heave-pitch equations of motion. Considering a ship floating on the free surface in waves. This ship will naturally heave and pitch due to the incident waves. It is not guaranteed that these two motions will be independent, however. Thus it becomes necessary to consider the motions together. The body boundary condition must be properly specified, thus we need to know both the linear and angular velocities of the vessel: G = dx 3 kr G dx 5 ± j = ( z x ² 5 , x ² 3 x x ² 5 ) (1) V B dt ± + × dt It follows that the velocity normal to the vessel hull is G ± V B nnz x ² 5 + n z ( x ² 3 x x ² 5 ) = n x ² 3 + ( n z n x ) x ² 5 (2) ⋅= x z x z G where the position vector, r , crossed with the unit outward normal, n ± , is n 4 n 5 = r G × n ± (3) n 6 version 1.0 updated 3/29/2005 -1- 2005, aht
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13.42 Spring 2005 In general the potential functions do not change significantly from our previous cases. However it
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r11_heavepitch - 13.42 Spring 2005 13.42 Design Principles...

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