Abstract
General solutions of differential equations of a ship motion, as they are linear nonhomogeneous with constant coefficients, are the sums of general solutions of homogeneous and of particular solutions of nonhomogeneous parts of equations (i.e. the sums of free and forced oscillations). Because of a damping which exists in the system, the general solutions of homogeneous parts of equations have an amortizing character. Therefore, it is usual in engineering practice to neglect the free oscillations and to suppose that the complete motion is reduced only to the forced oscillations.
The author attempts to find out a criterion for neglecting the free oscillations. Using the Routh-criterion the author proposed an unequality, which limits the magnitude of coefficient of damping δ. Taking this magnitude of coefficient δ we are allowed to assume that the complete motion of a ship is reduced to the forced oscillations only, whereas because then the free oscillations (provided long enough time t) approach zero.
It has b en supposed that the added masses and coefficient of damping are constants per unit of flotation surface.
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