A Consideration on the Coordinate System Used to Describe Sway and Yaw Motions of a Ship

Abstract

At present, both the coordinate axis fixed in the space and that fixed on a moving ship are used to almost the same extent when the sway and yaw motions of a ship are described. The former is preferred rather in the seakeeping study to treat ship motion in waves, and the latter is preferred in the study of ship manoeuvre in calm sea. So far, these two branches of ship dynamics have been developed independently of each other. In the near furture, however, we shall have to treat more frequently problems related to both seakeeping and manoeuvring. On the occasion, we shall be forced to make a due choice of the coordinate system, by which the equations of motion will be described. For this purpose, the author tries to throw light on the essential difference between the above-mentioned coordinate systems. In section 2, are compared the body-fixed coordinate axis and the space-fixed coordinate axis with each other by assuming that neither sway force nor yaw moment generate due to surging, heaving and pitching of a ship, and that sway force and yaw moment are represented as linear functionals of sway and yaw velocities of a ship. Furthermore in section 3, the same discussion is succeeded by attaching the condition of causality to the hydrodynamic force generated on a ship by its motion. As a result, it is ascertained that the body-fixed coordinate system is more suitable than the space-fixed coordinate system for clear understanding of physical nature of the hydrodynamic force.