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Logic Cloud
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To what extent do phase space trajectories describe a system? I often see classical systems being identified with (trajectories in) phase space, from which I get the impression these trajectories are supposed to completely specify a system. However, if you take for example the trajectory x^2+p^2=1 for a one-dimensional harmonic oscillator, it is still left open if x(t=0)=0 or x(t=0)=1 which corresponds to two different parameterizations of the circle. This leads me to ask: what is the role of phase space trajectories in the description of physical systems?