 Research on the SAM started as part of a 1982 senior thesis entitled "Smiles and Teardrops" (referring to the shape of some trajectories of the system) by Nicholas Tufillaro at Reed College, directed by David J. Griffiths.The swinging Atwood's machine is a system with two degrees of freedom.We may derive its equations of motion using either Hamiltonian mechanics or Lagrangian mechanics.