Trajectory Definition and 467 Threads

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of 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 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



(

f

k


(
x
)

)

k
∈

N





{\displaystyle (f^{k}(x))_{k\in \mathbb {N} }}
of values calculated by the iterated application of a mapping



f


{\displaystyle f}
to an element



x


{\displaystyle x}
of its source.

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