Trajekti

trajekti is the plural form of trajectory in several Slavic languages and is used to refer to the path that a moving object follows through space over time. In everyday language it describes the course of motion, while in technical contexts it carries a precise meaning tied to time parameterization.

In mathematics and physics, a trajectory is typically represented as a parametric curve r(t) in two or three dimensions, where t denotes time. The velocity is v(t) = dr/dt and the acceleration a(t) = d^2r/dt^2. The specific trajectory depends on initial conditions and the forces acting on the object, and may be designed or predicted using equations of motion or optimization techniques.

In physics and astronomy, trajectories arise from gravitational and other forces. Without drag, orbital trajectories are conic sections (ellipses, circles, parabolas, or hyperbolas). Real-world ballistic trajectories include air resistance and can be more complex. In differential geometry, curvature and torsion describe how a trajectory bends through space.

In engineering, robotics and computer graphics, trajectory planning involves designing feasible, optimized paths for moving bodies under constraints. In GIS and transportation analytics, trajectories refer to sequences of spatiotemporal coordinates collected from GPS or sensors and analyzed for movement patterns.

Etymology traces trajekt/trajekti to Latin and French roots meaning a forward throw or path. The term is used across disciplines to denote the path traced by a moving point as a function of time.