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Mathematical Model of Ship Motions in Irregular Sea in Problems of Synthesis of Radar Images



Need to assess the impact of moving objects on their radar images, as well as the need for the synthesis of algorithms of radar signals generated by moving objects causes the importance of developing a mathematical model of the observed objects. As an object of observation we considered six degrees of freedom vessels that defines the vibrations along the construction axes and the possible introducing moments about these axes. In general, the dynamics of the vessel can be reduced to the following: 1) the center of gravity of the ship movements (forward movement, heaving, surging and swaying – translational and oscillatory motion along the respective axes); 2) change the position of an object caused by - Rolling - rotational-vibrational motion in the transverse plane of the ship; - Pitching - rotational-vibrational motion in the longitudinal plane; - Yaw - rotational-vibrational movement in the horizontal plane. Based on consideration of the general problem of the theory of rolling, with nonlinear and nonstationary boundary conditions, using a linearization of the boundary conditions differential equations describing ship motions on the sea waves are given. It should be noted that when observing by radar with synthetic aperture antenna moving along the sea-surface objects, it is impossible to know exactly all the characteristics and parameters of the object, and in particular, such as loading a ship (its weight at the time of observation), alignment of the cargo, and so etc. In this connection the statistical approach to ships motions description in irregular sea waves. Thus, basing on a statistical approach and data of the test of series models in the experimental model basin of the Leningrad Shipbuilding Institute the implementation of ship motions on the sea waves for solving radiovision problems can be received.

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