= Closed orbit
A <closed orbit> returns to the same complete state and repeats its motion. For a nonconstant solution of an <autonomous differential equation> with unique solutions, $x(t+T)=x(t)$ for a positive period $T$ describes a <periodic orbit>. This usage excludes an <equilibrium point>, which is a stationary state rather than a moving cycle.
A <harmonic oscillator> has closed ellipses in its <phase plane>, because both <position> and <velocity> return after one oscillation. Returning to <position> alone is insufficient: a particle can pass the same point with a different <velocity>. A <bound orbit> also need not close; a <precessing orbit> can remain in a limited spatial region while changing its direction of closest approach. Specifying the complete state prevents a repeating projection from being mistaken for a repeating physical motion.
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