Abstract
The phase space time evolution operator for a dynamical system is derived directly from Newton’s equation of motion. This operator is used to show, in an elementary way, how a Lie group enters into the description in phase space of the path of a one-dimensional damped, driven, harmonic oscillator. Concepts from Lie group theory are thus illustrated in a nontrivial but elementary and familiar setting. Generalizations of this method for Hamiltonian systems are outlined in a series of remarks that suggest the broader scope of the subject.
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