Equations of Motion

This chapter gives a derivation of the equations of manoeuvring motion of a ship, first for axes fixed to the earth and then for axes fixed to the ship. Only motion in a horizontal plane is considered. (The equations for a body capable of linear motion along all three axes and angular motion about them are considered later in an appendix.) The equations of motionEquations of motion are used to obtain the Abkowitz modelAbkowitz model of ship manoeuvring and the concept of hydrodynamic derivativesHydrodynamic derivatives is introduced. Linearised equationsLinearised equations of manoeuvring are derived and the signs and magnitudes of the different linear hydrodynamic derivativesLinear hydrodynamic derivatives examined. The equations of motion for an arbitrary origin of coordinate are then derived. The non-dimensional forms of the equations and of the hydrodynamic derivatives in the Abkowitz model are also given.