Category:Definitions/Trajectories

This category contains definitions related to Trajectories.
Related results can be found in Category:Trajectories.

Trajectory of Body

Let $B$ be a body (which could be a particle) in motion.

The trajectory of $B$ is its path through the medium in which it is moving.

Trajectory of Dynamical System

Let $S$ be a dynamical system moving from point $A$ to point $B$.

The path taken by $S$ is known as the trajectory of $S$.

Trajectory of Point under Iteration

Let $f: S \to S$ be an iterated mapping on a set $S$.

Let $x \in S$ be a point of $S$.

The trajectory of $x$ under $f$ is the ordered subset of $S$ consisting of the points:

$\tuple {x, \map f x, \map {f^2} x, \ldots}$

where $\map {f^n} x$ is defined as $\map f {\map {f^{n - 1} } x}$, and so on.