MGSU RGR Dynamics

Theoretical Mechanics, Dynamics RGR, Moscow State Construction University, distance education http://cito.mgsu.ru
The mechanical system consists of four cylinders, interconnected inextensible cables. Rink 1 mass m1 radius rolling without slipping on a fixed plane inclined at an angle to the horizon. Blocks 2 and 3 - the same continuous homogeneous mass dual cylinders m2 = m3 c = inner radius r2 and the outer radius r3 R2 = R3. Given the moments of inertia Cylinder J2 = J3. Block 4 with radius and mass m4.
1. Using the general theorems of dynamics, create a system of equations describing the motion of a given mechanical system. Excluded from this system of equations of the internal forces, the differential equation, which serves to determine the dependence of s (t) coordinates of point A of the time - differential equation of motion of the system.
2. Get the same differential equation of motion of the system,
Using the theorem of change of kinetic energy of the mechanical
system in differential form.
3. The differential equation of motion of the mechanical system
on the basis of the general equation of dynamics.
4. Get the same differential equation of motion of the system,
reaching for her Lagrange equation of the 2nd kind.
5. Make sure the coincidence of the results obtained by four independent ways to integrate the differential equation of motion of the system, we obtain the dependence s (t) coordinates of point A of the time.
6. plotted M (t) and s (t)
7. Determine the tension cables at the initial time (t = 0).

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