A trajectory describes a body's position as it evolves with time, such as for a point mass. Its first time derivative is velocity and its second is acceleration. A geometrical path records which positions are visited; the time-parametrized trajectory additionally records how fast and in which direction the body moves along that path.
For a projectile in a uniform gravitational field without air resistance, horizontal uniform motion and vertical constant acceleration combine into a parabolic path. Changing the initial velocity selects a different trajectory even under the same force law. A phase-space trajectory retains momentum as well as position, so a particle passing through the same spatial point with different velocities occupies different phase-space states. Returning to one position alone therefore does not establish that the full motion is periodic.
Articles by others on the same topic
A trajectory is the path that a moving object follows through space as a function of time. It can refer to the motion of various types of objects, including projectiles, celestial bodies, vehicles, or any entity that is in motion. In physics and engineering, trajectories are typically analyzed within the context of forces acting on an object, initial velocity, acceleration, and other factors affecting motion.