The equations of a solid body motion

Abstract

Traditionally, the equations of motion of a solid body uses the theorem of the center of mass motion and the theorem of change of angular momentum with respect to the center of mass (Koenig’s axes). However, in the investigation of a solid body motion in a number of cases, the generalized coordinates are advisable to choose coordinates of another point of a body (pole) does not match the center of mass of the body, and the angles of rotation around this point. We obtain the equations of a solid body motion for these generalized coordinates. This is important for mathematical modeling of the motion of various objects, including vehicles. During the motion of a vehicle, its mass-inertial characteristics may change, including the position of the center of mass and the direction of the main axes of inertia, body mass and moments of inertia.