kinematisch

Kinematisch, or kinematik in German, is the adjective form of kinematic and is used to describe motion without reference to the forces that cause it. In physics, kinematisch analyses focus on how objects move: their positions, velocities and accelerations as functions of time, relative to a chosen frame of reference. The study applies to points, rigid bodies, and systems of particles and serves as a foundation for understanding motion in mechanics.

Core quantities in kinematisch analysis are position r(t) (or x(t), y(t), z(t)), velocity v(t) = dr/dt, and acceleration a(t) = d^2r/dt^2. For rigid bodies, angular kinematics uses angle θ(t), angular velocity ω(t) = dθ/dt, and angular acceleration α(t) = dω/dt, with velocity of a point on the body often described by translational motion plus rotational contribution. In planar motion, one may use Cartesian coordinates (x, y) or polar coordinates (r, φ). When acceleration is constant, common kinematic relations include r(t) = r0 + v0 t + (1/2) a t^2 and v^2 = v0^2 + 2 a · (r − r0).

Kinematisch analysis is frame-dependent, emphasizing relative motion between observers. It forms the basis for trajectory planning, motion tracking, and the geometric description of movement. Its applications span robotics, computer graphics and animation, biomechanics, vehicle dynamics, and surveying. Kinematisch is distinguished from dynamics, which also considers forces, torques, and energy that cause motion. In more advanced theories, kinematics extends to relativistic contexts, but its classical formulation remains central to many engineering and scientific problems.