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  2.6.2. Group of the FE with the phase shift which is distinct from zero

It is possible to organize work of group of the FE in such a manner that the beginning of a running cycle at each FE will differ from the previous FE.

Let's admit, phase shift at each FE from group        elements it will be equal

i.e., when the first FE from group begins a running cycle, last FE finishes it.

In a Fig. 17 the conditional scheme of work of group of the FE from 8 elements is presented.

Fig. 17

Let's admit, that each FE after end of a running cycle at once begins a new running cycle. Time of restoration of the FE in a working condition is lowered for simplification.

Mass of the mobile elements participating in movement in system from  FE:

,

At the  big number , i.e., accordingly, at small , it is possible to consider mass of the mobile elements participating in movement, a constant.

Average value of this mass:

, where Mass of one FE.

In a Fig. 18 the plot of  change of mass of mobile elements of system from 4 FE is presented.

Fig. 18

The center of mass of each of the FE moves on dependence (8).

,

The plot of moving of the centers of mass of mobile elements of system from 4 FE is presented in a Fig. 19.

Fig. 19

The sum of linear momentums of the FE of the coordinates system connected with closed mechanical system, is defined by expression:

In a Fig. 20 the plot of change of a linear momentum of system of the FE with phase shift is presented.

Fig. 20

Average value of a total momentum of the FE in mobile coordinates system will be:

 Mass  of a part of mechanical system with which center of mass the reference mark of mobile coordinates system is connected XOY.

 Speed of mobile coordinates system XOY in a projection to an axis Y motionless coordinates system XOY.

 Mass of mobile elements of the FE .

Part of expression:

    Defines a momentum of the FE in motionless coordinates system XOY.

The decision of the differential equation (45) rather , in view of entry conditions:

 (initial speed of system is equal to zero),
 gives following result:

The analysis of expression (46) shows, that system from  The FE, the beginning of a running cycle of each of which differs from the beginning of a running cycle of the previous FE on size , moves in regular intervals (a Fig. 21).

In a Fig. 21 red color represents a trajectory of movement of system from three FE.
(At , curve  in a Fig. 21 comes nearer to a straight line.  Though and for n=3 the curve not so strongly differs from a straight line!)

Fig. 21

Calculation is made of a condition, that each FE after end of a running cycle at once begins a new running cycle. Time of restoration of the FE in a working condition is lowered for simplification.

The system moves in regular intervals only at  .

Speed of all closed system is a derivative on time from the coordinate defining the center of mass of system:

Acceleration of system as a derivative on time from speed, it is equal to zero:

That is, at any moment the system moves without acceleration.

It is possible to calculate force from which the system of the FE is capable to move all mechanical system.

The force developed by one FE  is certain above (38):

For group of the FE with phase shift total force:

At a plenty of the FE in group, it is possible to accept average value of total force:

By analogy to gyroscopes at which the gyroscopic moment is result Coriolis  forces of inertia, at the FE force of moving is result of centripetal forces of inertia.

At continuous group work each FE changes the kinetic energy (39).

For a time unit, quantity of the "lost" energy it is equal to quantity of the energy transferred by the FE for restoration. At big  and continuous restoration of the FE, it is possible to consider work on restoration of the FE uniform.

The capacity necessary for restoration of the FE in a working condition:

The note:

 Value of capacity is found from a condition, that elements of mobile systems of the FE completely stop after end of a running cycle. In real devices it to do it is inexpedient. It is recommended to change speed of mobile elements only on one coordinate.

In that case, it is possible to use a stock of kinetic energy of system of mobile elements for translation of the FE in a working condition. Thus value (49) will be it is much less.

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