Trajectories

A trajectory or flight path is the path that a moving object follows through space as a function of time. The object might be a projectile or a satellite. For example, it can be an orbit—the path of a planet, an asteroid, or a comet as it travels around a central mass. A trajectory can be described mathematically either by the geometry of the path or as the position of the object over time.

In control theory a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map). In discrete mathematics, a trajectory is a sequence ${\displaystyle (f^{k}(x))_{k\in \mathbb {N} }}$ of values calculated by the iterated application of a mapping ${\displaystyle f}$ to an element ${\displaystyle x}$ of its source.

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