Kinematika

Kinematics, known in some languages as kinematika, is the branch of classical mechanics that describes the motion of objects or systems without considering the forces that cause the motion. It focuses on how position, velocity, and acceleration change over time within a chosen frame of reference.

The basic quantities include position r(t) or x(t), displacement Δx, speed (scalar) and velocity (vector), and acceleration (vector). For rotational motion, angular position θ(t), angular velocity ω, and angular acceleration α are used. Motions are described in coordinate systems such as Cartesian, cylindrical, or spherical coordinates.

In one dimension with constant acceleration a, the standard kinematic equations relate initial velocity v0, final velocity v, displacement s, and time t: v = v0 + a t, s = v0 t + 1/2 a t^2, and v^2 = v0^2 + 2 a (s − s0). In three dimensions, these relations are written in vector form: v = dr/dt, a = dv/dt, and s(t) is obtained by integration.

Rotational kinematics treats θ, ω, and α with analogous equations: ω = dθ/dt, α = dω/dt, and θ = θ0 + ω0 t + 1/2 α t^2. For constant α, ω = ω0 + α t and θ = θ0 + ω0 t + 1/2 α t^2. For rigid bodies, translational and rotational motions can be analyzed separately or combined.

Kinematics underpins many fields, including robotics, computer animation, biomechanics, and vehicle dynamics, and it provides the framework for solving problems about motion in engineering and physics. Its historical roots trace to early studies by Galileo and later formalization in Newtonian mechanics.