TABLE OF CONTENTS Solution of the equations of motion as written above yields the motions of the reference point on the moving body. We are often more interested in motions at some other point on the body, such as the bridge on a ship or the helicopter landing area on a platform. In addition, relative motions between the wave crests and certain points on the body are of extreme importance in design: For ships, water shipping and propeller emergence, for example, depend on relative vertical motions, and slamming depends on relative vertical velocity; for platforms, designers try to minimize wave contact with the deck cross-structure.
Recall that the location of a point P on a moving body relative to a fixed coordinate system is given by
where R is the location (position vector) of the origin of the body axes and ?(P) gives the location of the "point of interest" relative to this origin. Since the components of ? are usually known constants relative to body axes (we can regard the ship or structure as a rigid body in most seakeeping analyses), we need to apply the transformation of Eq. (1.7) to find the location of the point relative to the fixed (or steadily translating) ??? system:
The transformation matrix T is given by Eq. (1.8), which simplifies to the form given in Eq. (2.21) for small-amplitude motions.
The velocity and acceleration of point P are found by differentiating Eq. (5.209)...
