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phase space be explicitly diagrammed as in Figure 3-2. The trajectory in two- dimensional phase space, representing the time development of the system, corresponds to the set of parametric equations. q=q(t), p=p(t). For a linear harmonic oscillator with constant energy ε the phase-space trajectory corresponds to an ellipse in the p-q plan (Blinder, 1969) p p2 kq2 2m 2 q 32 Figure 3-2: Trajectory in two-dimensional phase space The analogous representation of more complex system mechanical systems, even with n~1024, introduces no additional conceptual difficulties, notwithstanding the multidimensionality of the corresponding phase space. The trajectory is, in the general case, determined by the 2n equations qi=qi(t), pi=pi(t) i=1...n. These are, in turn, determined by classical Hamiltonian’s equations of motion . H . H qi p , pi q i=1...n ii in conjugation with 2n initial values qi(0), pi(0). The Hamiltonian function H(q1...qn,p1...pn) for a multidimensional system will be for convenience, abbreviated H (p,q) and dot denotes the time derivative. It expresses the total energy of an isolated system as a function of the coordinates and momenta of the constituentPDF Image | MOLECULAR SIMULATION STUDIES IN THE SUPERCRITICAL REGION
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