Find: in

  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):

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 .
Other bodies of system continue to move up to full , i.e., up to a filling angle aperture .

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.
(The note. The imposed restriction is quite admissible, as can be realized for conditions of the closed system. See section 2.5)

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.


// //
Сайт создан в системе uCoz