Trajectory

A trajectory is the path an object takes through its motion over time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.

The object as a mass might be a projectile or a satellite. For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.

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.