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The motion of marine vessels has traditionally been studied using two different approaches: manoeuvring and seakeeping. These two approaches use different reference frames and coordinate systems to describe the motion. This paper derives the kinematic models that characterize the transformation of motion variables (position, velocity, accelerations) and forces between the different coordinate systems used in these theories. The derivations hereby presented are done in terms of the formalism adopted in robotics. The advantage of this formulation is the use of matrix notation and operations. As an application, the transformation of linear equations of motion used in seakeeping into body-fixed coordinates is considered for both zero and forward speed

Kinematic Models for Manoeuvring and Seakeeping of Marine Vessels