This Demonstration determines the solution of a discrete system of two cylinders connected by three springs. You can adjust the mass of each cylinder and the stiffness of each spring to see the effect on the dynamics of the system. The left and right cylinders have masses
, respectively. The spring stiffness values are
from left to right. You can adjust the initial angular velocity of either cylinder. The initial angular position is assumed to be zero. The equations of motion are derived using the Lagrangian method. The author
contains the mathematical derivation of the equations of motion. Cylinders roll without slipping and the system has two degrees of freedom
. The system potential energy, kinetic energy, and total energy are displayed in the table at the top. Since zero friction and damping are assumed, the total energy remains constant.