trajektore

Trajektore is a term used in several Slavic languages to denote trajectories—the paths that moving objects or evolving states follow through space and time. In English, a trajectory is typically described as a parametric curve γ(t) = (x(t), y(t), z(t)) giving the position at time t. The speed and direction are given by the first derivative γ'(t), and the acceleration by γ''(t).

In mathematics, a trajectory can be the integral curve of a vector field or the solution to a differential equation. It represents the evolution of a system's state over time and may be constrained to avoid obstacles or satisfy control limits.

In physics and engineering, trajectories appear in projectile motion, celestial mechanics, fluid flows, and robotic motion planning. In orbital mechanics, a planet or satellite follows a conic section around a primary body; in robotics, planners generate feasible trajectories under velocity and acceleration limits.

In data science and computer graphics, trajectory data record the positions of moving objects or cameras. Analyzing trajectories involves tasks such as smoothing, interpolation, prediction, and clustering by similarity.