Modeling Crane Induced Ship Motion Using the Moving Frame Method

Abstract

A decline in oil-related revenues challenges Norway to focus on new types of offshore installations and their maintenance. Often, ship-mounted crane systems transfer cargo or crew onto marine structures such as floating windmills. This project analyzes the motion of a ship induced by an onboard crane in operation. It analyzes the motion of a crane mounted on a ship using The Moving Frame Method (MFM). The MFM draws upon Lie group theory and Cartan’s Moving Frames. This, together with a compact notation from geometrical physics, makes it possible to extract the equations of motion, expeditiously. This work extends a previous project that assumed many simplifications. It accounts for the masses and geometry of all components. This current approach also accounts interactive motor couples and prepares for buoyancy forces and added mass. The previous work used a symbolic manipulator, resulting in unwieldy equations. In this current phase, this research solves the equations numerically using a relatively simple numerical integration scheme. Then, the Cayley-Hamilton theorem and Rodriguez’s formula reconstructs the rotation matrix for the ship. Furthermore, this work displays the rotating ship in 3D, viewable on mobile devices. WebGL is a JavaScript API for rendering interactive 3D and 2D graphics within any compatible web browser without the use of plug-ins. This paper presents the results qualitatively as a 3D simulation. This research proves that the MFM is suitable for the analysis of “smart ships,” as the next step in this work.