kinematik

Kinematik, or kinematics in English, is the branch of classical mechanics that studies the motion of bodies without considering the forces that cause the motion. It describes how position, velocity, and acceleration of objects evolve in time and in space, using reference frames and mathematical descriptions of trajectories.

Key quantities include the position vector r(t), displacement, velocity v = dr/dt, speed, and acceleration a = dv/dt. Time is the independent variable, and motion can be analyzed in one, two, or three dimensions. It is important to distinguish scalar speed from vector velocity, and to consider instantaneous values as well as averages. A trajectory is the path followed by the moving object.

Equations of motion in kinematics relate these quantities. In one dimension with constant acceleration a, s = s0 + v0 t + 1/2 a t^2; v = v0 + a t; v^2 = v0^2 + 2 a (s − s0). In higher dimensions, the position vector r(t) describes the path, with v = dr/dt and a = dv/dt. Graphical methods often use position-time, velocity-time, and acceleration-time plots to analyze motion.

Rotational kinematics treats angular quantities: angular position θ(t), angular velocity ω = dθ/dt, and angular acceleration α = dω/dt. For constant α, θ = θ0 + ω0 t + 1/2 α t^2; ω = ω0 + α t. Linear quantities relate to angular ones via r: v_t = r ω, a_t = r α, a_r = r ω^2.

Kinematics underpins fields such as robotics, computer graphics, biomechanics, astronomy, and vehicle dynamics. It provides a descriptive framework for motion, while dynamics addresses the forces and energy that produce it.