Abstract
In order to derive the marine craft equations of motion, it is necessary to study the motion of rigid bodies, hydrodynamics and hydrostatics. This chapter shows that the rigid-body kinetics can be expressed in a vectorial setting according to (Fossen, 1991). The rigid-body equations of motion will be derived using the Newton-Euler formulation and vectorial mechanics. In this context it is convenient to define the vectors without reference to a coordinate frame. For marine craft it is desirable to derive the equations of motion for an arbitrary origin CO (origin Ob of {b}) to take advantage of the craft's geometric properties. Since the hydrodynamic forces and moments often are computed in CO, Newton's laws will be formulated in CO as well. The chapter discusses the useful properties of the equations of motion and demonstrates how these properties considerably simplify the representation of the nonlinear equations of motion. Controlled Vocabulary Terms hydrodynamics; marine vehicles; mechanical properties; motion control; reaction kinetics
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