AN ALGORITHM FOR CONSISTENT LINEARIZATION OF SHIP MANOEUVRING MATHEMATICAL MODELS

A numerical algorithm for flexible linearization of substantially nonlinear ship mathematical models described by ordinary differential equations is proposed. The linearization can be performed over any pre-defined domain in the state space or subspace in the least-square sense. A discrete set of points is created inside the domain of interest by means of a quasi-random sequence generator. Then, the exact model's responses are calculated on this set and a common least-square procedure is applied. Local or differential linearization can be performed with the same algorithm choosing an appropriately small domain around any point of interest in the state space. A numerical example for a typical directionally unstable vessel is given and studied is the influence of the number of the generated quasi-random points and of the linearization domain's dimensions.