Kinematiikan

Kinematiikan, or kinematics in English, is a branch of classical mechanics that describes the motion of objects without regard to the forces that cause that motion. It analyzes how position, velocity, and acceleration change over time and uses mathematical models to predict trajectories.

The primary quantities are position r(t) (or x(t) in one dimension), velocity v(t) = dr/dt, and acceleration a(t) = dv/dt. Displacement is the change in position, Δr. Quantities can be scalars (speed, distance) or vectors (position, velocity, acceleration).

In uniform or nonuniform motion, kinematics employs equations of motion. For constant acceleration in one dimension: s = ut + 1/2 a t^2, v = u + a t, and v^2 = u^2 + 2 a s. In multiple dimensions, these become vector equations with r(t) and a(t).

Rotational kinematics covers angular position θ(t), angular velocity ω = dθ/dt, and angular acceleration α = dω/dt. Linear relations include v = r ω and a_t = r α, with radial (centripetal) acceleration a_r = r ω^2. Motion is often described in coordinate systems such as Cartesian, cylindrical, or spherical.

Kinematics is distinguished from dynamics; it describes motion without explaining causes. It assumes inertial frames of reference and is extended by relativity at high speeds. Applications include robotics (forward and inverse kinematics), computer graphics, biomechanics, sports science, and astronomy.