On the nonlinear uncoupled roll and pitch of submerged vehicles

This paper presents an exact solution of the problem of free nonlinear rolling or pitching motion of a submerged vehicle. The nondimensional frequency-amplitude relationship of free uncoupled roll or pitch is universal, i.e. the single curve describes the behavior of any vehicle. This relationship is softening, i.e. the decreasing frequencies correspond to larger amplitudes of roll or pitch. The amplitudes of vibrations in the region of frequencies corresponding to the resonance are very sensitive to small variations of the frequency. These conclusions, i.e. the softening nonlinearity and the high sensitivity of the amplitudes to small variations of the vibration frequency are valid also for the problem of forced nonlinear roll or pitch motion of submerged vehicles.