Dynamics of relative motion

Abstract

Let us consider a material system consisting of “carrying” rigid body and N “carried bodies” which are particles whose position with respect to axes Oxyz, fixed in the “carrying body” can be described by a finite or even a countable set (the case of a solid) of the generalised coordinates. While investigating the motion of such a system we can state two problems. The first problem is as follows. The motion of the “carrying body” is prescribed and the motion of the “carried bodies” is required under the assumption that the motion of the “carried bodies” does not affect the prescribed motion of the carrying body. The position of the system can be defined by n independent generalised coordinates q _s , the case of a solid included. Particularly, such a motion can occur when the mass of the carrying body is much greater than the masses of the carried bodies and their influence on the motion of the carrying body can be neglected. For example, the influence of a gyroscope on the motion of the earth can be unconditionally neglected. However the motion of the earth influences the motion of the gyroscope considerably. It is clear that this case can occur when the prescribed motion of the carrying body is caused by external forces. These forces can be determined from the equations of motion.