Trajectory

A Trajectory is the path of a moving object in space decribed as a function of time.

• AKA: Path of Motion.
• Example(s):
  • Orbit.
• Counter-Example(s):
  • Velocity.
  • Acceleration.
• See: Moving Object, Path, Linear Motion, Circular Motion.

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References

2015

• (Wikipedia, 2015) ⇒ http://www.wikiwand.com/en/Trajectory
  • QUOTE: 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 [math]\displaystyle{ (f^k(x))_{k \in \mathbb{N}} }[/math] of values calculated by the iterated application of a mapping[math]\displaystyle{ f }[/math] to an element [math]\displaystyle{ x }[/math] of its source.

2009

• (Monreale et al., 2009) ⇒ Anna Monreale, Fabio Pinelli, Roberto Trasarti, and Fosca Giannotti. (2009). “WhereNext: A Location Predictor on Trajectory Pattern Mining.” In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD-2009). doi:10.1145/1557019.1557091
  • QUOTE: The prediction uses previously extracted movement patterns named Trajectory Patterns, which are a concise representation of behaviors of moving objects as sequences of regions frequently visited with a typical travel time. A decision tree, named T-pattern Tree, is built and evaluated with a formal training and test process. The tree is learned from the Trajectory Patterns that hold a certain area and it may be used as a predictor of the next location of a new trajectory finding the best matching path in the tree.

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