Palautumiskerroin

Palautumiskerroin, or coefficient of restitution (abbreviated e), is a dimensionless parameter that characterizes how elastic a collision between two bodies is. It describes the ratio of the relative speed of separation to the relative speed of approach along the line of impact.

Formally, if two bodies approach with velocities u1 and u2 and separate with velocities v1 and v2, and n is the unit normal along the line of impact from body 1 to body 2, then e = - (v2 − v1) · n / ( (u1 − u2) · n ). In words, e is the ratio of the magnitude of the relative normal velocity after collision to that before collision. Values typically lie between 0 and 1 for real collisions: e = 1 corresponds to a perfectly elastic collision (no kinetic energy lost in the normal direction) and e = 0 corresponds to a perfectly inelastic collision (the bodies stick together in the normal direction). Values greater than 1 are not physical for standard collisions without external energy input or definitional nuances.

Measurement and factors: e can be estimated experimentally, for example by dropping a ball onto a rigid surface and measuring bounce height. If the ball is dropped from height h0 and rebounds to height h1, then e ≈ sqrt(h1/h0). Real-world e depends on materials, surface roughness, spin, energy split into rotation and vibration, temperature, and impact velocity; it may vary with conditions and is not always constant.

Applications: used in rigid-body dynamics, collision simulations in engineering and computer graphics, sports equipment design, and the study of granular materials to predict post-collision motion. See also coefficient of friction and impulse.