2.1. Target setting
For the closed system, i.e. the system which are not testing external influences, or in case of when the geometrical sum of external forces acting on system is equal to zero, the principle of conservation of momentum takes place. Thus a linear momentum of separate parts of system (for example, under action of internal forces) can change, but so, that size remains a constant.
Let's consider a following task ( Fig. 1):
Around of the center of mass of a massive body , on a circle of radius R the system of bodies in total mass moves with constant speed . The system of bodies is distributed continuously and in regular intervals. The trajectory of movement of system of bodies is rigidly connected with a body .
Moving of this system of bodies can be considered, how rotation of a body with mass with constant angular speed w concerning some center. We shall assume, for simplification, that each element has the infinitesimal geometrical sizes.
At the certain moment of time
the chain bodies is broken off. Each element
of system begins stops in a point with coordinates . A stop of separate elements it is considered, how not
elastic impact after which elements get speed of a body
Word-combination - "filling angle aperture" , in this case, we shall understand a angle counted from an axis OX up to a closing element of system body.
At the initial moment of time : (for the given task).
The filling angle aperture changes from 0 up to 2 π:
Time for which the filling angle aperture varies from 0 up to 2 π , let's name the working period, or a running cycle T .
Let's consider, that all mechanical
system has two degrees of freedom (moving on axes X and Y).
We shall accept a condition that there is a restriction
of turn of all system.
Let's construct two coordinates systems: motionless XOY (absolute coordinates system) and mobile XOY, connected with the center of mass and with the center of a trajectory of mobile elements.