 Orbit (dynamical system)

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.