Modeling of plane-parallel motion of a vessel based on a nonlinear dynamic system with varying parameters using the perturbation method and its experimental verification

The analytical solution of a nonlinear dynamic system, which is a model of plane-parallel motion of a vessel, was obtained by the perturbation method. The solutions obtained allow us to take into account the influence of all the main parameters on linear and angular velocities. Small parameters are analyzed, the choice of which is determined by the specific parameters of the task. The influence of linear velocity on angular velocity due to the nonlinearity of the back is shown. The influence of the static moment on each of the velocity components is shown. The influence of salinity and temperature and, consequently, density on the parameters of the system and, as a result, on the speed of the vessel is considered. The effect of salinity is considered in the form of a piecewise constant function and a piecewise linear function. A modification of the solutions for velocities is shown, which must be done to clarify their values in different sections of the trajectory. An analytical and numerical method for modeling the plane-parallel motion of a vessel is proposed, taking into account the influence of heterogeneity of the water basin on the basis of hydrometeorological data. The obtained solutions can be used to automate the movement of a vessel along a limited fairway using an automatic control system.