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Chapter 33
Unresisted rolling in
still water
A ship will not normally roll in still water but if a study be made of such rolling some important conclusions may be reached. For this study it is assumed that the amplitude of the roll is small and that the ship has positive initial metacentric height. Under the conditions rolling is considered to be simple harmonic motion so it will be necessary to consider brie¯y the principle of such motion.
Let XOY in Figure 33.1 be a diameter of the circle whose radius is `r' and let OA be a radius vector which rotates about O from position OY at a constant angular velocity of `w' radians per second. Let P be the projection of the point A on to the diameter XOY. Then, as the radius vector rotates, the point P will oscillate backwards and forwards between Y and X. The motion of the point P is called `Simple Harmonic'.
Fig. 33.1
