Kinematic

Kinematic is an adjective used in physics and engineering to describe aspects of motion without reference to the causes or forces responsible for that motion. It encompasses the study of how objects move, including their position, displacement, velocity, acceleration, time, and orientation, described within a chosen frame of reference. The term is often used in contrast to dynamics, which focuses on forces and energy.

Key concepts in kinematic analysis include position r(t) and time, displacement Δr, speed or scalar magnitude of velocity v = dr/dt, and acceleration a = dv/dt. Motion can be described in one, two, or three dimensions, and involves both magnitude and direction. In linear motion with constant acceleration, common equations relate displacement, initial velocity, final velocity, and time, such as v^2 = u^2 + 2as and s = ut + 1/2 at^2. In rotational or angular motion, angular displacement, angular velocity, and angular acceleration describe motion about an axis, with linear quantities linked by v = rω and s = rθ.

Applications of kinematic analysis occur across physics, engineering, robotics, computer animation, biomechanics, and vehicle dynamics. In robotics, forward kinematics computes the position of an end-effector from joint angles, while inverse kinematics seeks joint configurations for a desired end position. Kinematic methods provide the geometric foundation for understanding motion before incorporating forces, masses, and energy in dynamic analysis.