A trajectory or flight path is the path that a mass moving object follows through space as a function of time. In classical mechanics, it is generally a continuous, derivable curve in three-dimensional Euclidean space. It can be derived from the law of time by separating it into the parametric equations in time of the three extrinsic coordinates, while the reverse is not possible since there is no velocity information in the trajectory.
Some of the most common types of trajectories are straight trajectory, parabolic trajectory, elliptical trajectory, circular trajectory, and helical trajectory.
- Straight Trajectory: This is the trajectory described by a body moving along a straight line, such as a train moving along a straight track. This type of trajectory is typical of uniform rectilinear motion and uniformly accelerated rectilinear motion.
- Parabolic trajectory: Any trajectory that has the shape of a parabola; the most classic example of a parabolic trajectory is that described by the motion of a projectile.
- Elliptical trajectory: any curved trajectory of elliptical shape described by the motion of a material point; an example of an elliptical trajectory is the orbit of the planets around the sun (as established by Kepler’s first law).
- Circular trajectory: a trajectory described by a body moving along a circumference, as occurs in uniform circular motion and uniformly accelerated circular motion.
- Helical trajectory: A trajectory that has the shape of a helicoid. An example of a helical trajectory is that of a charged particle immersed in a magnetic field.