LAUSR

A generalized model of the Atwood machine when two bodies can swing in a plane is considered. Combining symbolic and numerical calculations, we have obtained equations of motion of the system and analyzed their solutions. We have shown that oscillations can completely modify motion of the system while the simple Atwood machine demonstrates only the uniformly accelerated motion of the bodies. In particular, a quasi-periodic motion of the system can take place even in case of equal masses of the bodies. We have also obtained a differential equation determining an averaged translational motion of the system and have shown that its solution corresponds completely to the numerical solution of the exact differential equations of motion. The validity of the results obtained is demonstrated by means of the simulation of motion of swinging Atwood’s machine with the computer algebra system Wolfram Mathematica.