= Orbit
{disambiguate=dynamical system}
{wiki=Orbit_(dynamics)}
= Orbit
{synonym}
An <orbit> is the set of states reached from one initial state under a <dynamical system>'s evolution. A <forward orbit> restricts attention to future times; a complete <orbit> includes backward times when the model admits them. Keeping the <time> ordering gives a <trajectory>, while forgetting the parameter emphasizes the geometry of the visited set.
For a <harmonic oscillator>, the <phase plane> <orbit> is an ellipse determined by its <mechanical energy>. The particle repeatedly visits the same <positions>, but its full state distinguishes motion in opposite directions. A damped oscillator instead approaches an <equilibrium point> along a spiralling or nonoscillatory <orbit>, depending on its parameters. The state-space description is therefore broader than a spatial orbital path: the variables can describe velocities, temperatures or populations as well as physical <positions>.
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