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ON THE NORMAL MODES OF NONLINEAR COUPLED SHIP MOTIONS AND THEIR STABILITY
CALIFORNIA UNIV BERKELEY INST OF ENGINEERING RESEARCH
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The concept of normal oscillations of a nonlinear conservative system is introduced and applied to the ship motion problem. In addition the stability of these normal modes is investigated and found to depend in general on the same parameters given in previous investigations. Since the normal oscillations represent a combined motion in the degrees of freedom concerned, an unstable mode does not necessarily imply unbounded motion in any one of the degrees of freedom. Since the system is assumed to be conservative, all displacements are necessarily finite. A knowledge of those straight normal modes which are stable is important since it is reasonable to conclude that the motion of ships in calm water will take place near those normal modes. In the absence of damping, the system is conservative, and hence the total energy of the system is a constant. This implies that all displacements and velocities must be finite. Because damping is always present, the system must ultimately reach a stable equilibrium position since energy is constantly dissipated from the system. Author
APPROVED FOR PUBLIC RELEASE