ASSESSMENT OF THE IMPACT OF THE DISPLACEMENT OF THE CENTER OF MASS OF THE FREE-FALL LIFEBOAT RELATIVE TO THE SUPPORT SURFACE ON ITS MOTION WHEN DROPPING FROM THE SHIP

Abstract

The problem of the motion of free-fall lifeboats (FFLB) when dropping from the ship, taking into account the displacement of the center of mass relative to the supporting surfaces during the rotation phase – from the moment when the center of mass of the boat is above the edge of the support (extreme roller of the ramp) until the end of the supporting surfaces of the boat leaves the ramp. To compile the differential equations of motion of the FFLB during the phase of rotation, the Lagrange equation of the second kind in the polar coordinate system (differential equations of flat-parallel motion of the boat in generalized coordinates, where r is the distance from the edge of the support to the projection of the center of mass on the support surface and φ- the angle of inclination of the supporting surface of the boat to the horizon) is applied.

The solving system of two ordinary nonlinear differential equations of the second order is obtained and the corresponding Cauchy problem is formulated, which is solved numerically using the Runge-Kutta method of the fourth order of accuracy.

The approbation of the developed approach was carried out for the case of modeling the boat with a homogeneous rod in the form of a rectangular parallelepiped with length L and thickness h. The corresponding solving system of four ordinary nonlinear differential equations of the first order in the Cauchy form in generalized coordinates r i φ was obtained, for which the Cauchy problem was formulated, which was solved numerically by the Runge-Kutta method of the fourth order of accuracy at the angle of inclination of the ramp α=35° for rods with a thickness of 0; 0,2; 0,4; 0,6; 0,8; 1.0 m and a length of 5, 10 and 15 m at initial speeds of 6, 8 and 10 m/s, respectively. The results of calculations of the duration of the phase of rotation, the angle of inclination and pitch angle, radial and angular velocity, the speed of the center of mass and its vertical and horizontal components, the angle of inclination of the vector of the speed of the center of mass to the supporting surfaces of the boat indicate that when the center of mass is located above the supporting surface of the guide beam, an increase in its distance to the supporting surface leads to an increase in all parameters of the RSVP motion at the end of the rotation phase. At the same time, the effect of displacement increases with a decrease in the length of the boat (the moment of inertia relative to the center of mass). Based on the results of the work, it was concluded that it was possible to use the proposed approach and conduct numerical experiments for the rational choice of the parameters of the RSHVP motion and the directions for further research were determined.