The thermodynamic and kinetic properties of Lennard-Jones homopolymers are studied by computer simulation of the homopolymer at constant temperature and during collapse following an abrupt temperature drop. The homopolymer dynamics is simulated using both the Gaussian phase packet dynamics algorithm, which provides an approximate solution of the Liouville equation for the time dependent classical density distribution, and conventional molecular dynamics. Numerical simulations of both linear and ring polymers are analyzed and compared with theoretical predictions. The results support the idea that homopolymer collapse is a two-stage process.