The solution to the problem of D9 Option 99 Reshebnik on theoretical mechanics manuals SM Targ 1983.
Specifying Conditions D9 (p. 60-63 zadachnik Targ SM 1983):
The mechanical system consists of one step u2 weight pulleys P1 and P2 stages with radii R1 = R, r1 = 0,4R; R2 = R, r3 = 0,8R (weight of each pulley assumed to be uniformly distributed along its outer rim); loads 3, 4 and a solid cylindrical roller homogeneous 5 weight P3, P4, P5, respectively (Fig. Table D9.0-D9.9. D9). Body systems are connected strands wound on pulleys; Lots of threads parallel to respective planes. Loads of slides on the plane without friction rollers and rolling without slipping.
In addition to the forces of gravity on one of the bodies of the system constant force F, and the pulleys 1 and 2 in their rotation are constant moments of resistance forces, which are equal to M1 and M2.
Create for the system Lagrange equation and determine from it the amount specified in the table in the column "Find", where indicated: ε1, ε2 - angular acceleration of the pulleys 1 and 2; a3, a4, AC5 - acceleration of goods 3, 4 and the center of mass of the roller 5, respectively. As for the problem to be determined ε1, ε2, assume R = 0,25 m.
One of the weights 3, 4 by weight is equal to zero, the drawing does not depict. Pulleys 1 and 2 are always part of the system.
Task D9 - by application to the study of the Lagrange equation of motion of the system.