Abstract
In the problems of naval hydromechanics it is quite common to use the linearity assumption. Although this simplification eases the difficulties encountered in solving the problems, it also hinders some important features of the systems. Large amplitude rolling motion and steering of a ship, and vibration of an elasto-plastic system are typical examples of physical problems for which nonlinearity is to be taken into account. Today there are a number of methods with varying complexity for the approximate solution of ordinary differential equations. Depending on the type of the problem and the requirements on the sought solution one of these methods may be utilised. In this manuscript a variational method due to Bubnov and Galerkin is presented which has the advantages of preserving the equations of motion and minimising the total error. Application of the method is illustrated for large amplitude rolling motion of a ship.
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