Pályavonalak

Pályavonalak are lines that represent the trajectory or path of a moving object or particle within a given field or space. The term is used across several disciplines, including physics, engineering, geography, and computer science, to describe the locus traced by motion over time or through space.

In physics and fluid dynamics, pályavonalak may refer to pathlines, streamlines, or streaklines, depending on the context. A pathline is the actual trajectory of a single particle as time advances, obtained by solving dr/dt = v(r,t) with an initial position r(t0) = r0. A streamline is an instantaneous line tangent to the velocity field at a fixed time, while a streakline is the set of particle positions that passed through a common point at a certain time. Pályavonalak is a generic term that may denote any of these in descriptive writing.

In astronomy, pályavonalak describe orbital trajectories of celestial bodies, projected paths with respect to a primary body. In robotics and computer graphics, a pályavonal is the planned or generated motion path of a robot or camera, often computed to satisfy constraints such as obstacles, speed, and smoothness.

Mathematically, if r(t) denotes the position of a moving point, the pályavonal is the set {r(t) | t in [t0, t1]}. The concept helps visualize motion patterns, analyze transport, and plan routes.

See also: pálya, trajektória, útvonal, vonal, útvonalak.