The swinging variety is only integrable when the stationary element is three times as massive; otherwise, the motion it exhibits is chaotic.
The swinging variety is only integrable when the stationary element is three times as massive; otherwise, the motion it exhibits is chaotic. In the simplest case, the acceleration of the system is equal to g times the difference of the masses over the sum of the masses; similarly, the tension in the string connecting the two masses is equal to g times twice the product of the masses over their sum. Invented by its namesake to prove Newton's laws, this is, FTP, what simple apparatus that consists of two or more masses connected by a massless string on frictionless pulleys?
The swinging variety is only integrable when the stationary element is three times as massive; otherwise, the motion it exhibits is chaotic.
{Atwood's machine}