Kinematics

Lore & Background

Kinematics studies the geometrical aspects of motion of physical objects independent of the forces that set them in motion. It deals with quantities such as position, distance, and angular measure with respect to a frame of reference, and most frequently with the time derivatives of these quantities and the relations between them. Objects studied include points and subsets of Euclidean space that undergo rigid motion. Constrained motion, such as linked machine parts, is also described as kinematics. Systems of specification include rectangular Cartesian coordinates, curvilinear coordinates like polar coordinates, and other systems. Object trajectories may be specified with respect to other objects that may themselves be in motion relative to a standard reference, and rotating systems may also be used. The scholar Ibn al-Haytham is credited with being the first to treat geometry and kinematics as a unified concept, comparing the dimensions of a body when in motion versus when at rest.

Reader's Guide

Kinematics is foundational to classical mechanics and is used across multiple disciplines. In astrophysics, it describes the motion of celestial bodies and collections of such bodies. In mechanical engineering, robotics, and biomechanics, kinematics describes the motion of systems composed of joined parts, such as an engine, a robotic arm, or the human skeleton. Geometric transformations, including rigid transformations, are used to describe the movement of components in a mechanical system, simplifying the derivation of equations of motion. Kinematic analysis measures kinematic quantities to find the range of movement for a given mechanism, while kinematic synthesis designs a mechanism for a desired range of motion. Kinematics also applies algebraic geometry to the study of mechanical advantage. Relativistic kinematics applies the special theory of relativity, encompassing time dilation, length contraction, and the Lorentz transformation, operating in a spacetime geometry where spatial points are augmented with a time coordinate to form 4-vectors. Werner Heisenberg reinterpreted classical kinematics for quantum systems, showing that classical kinematic notions like velocity and energy are valid in quantum mechanics, but pairs of conjugate kinematic and dynamic quantities cannot be simultaneously measured, a result known as the uncertainty principle.

Did You Know?

• The term 'kinematic' is the English version of A.M. Ampère's 'cinématique', constructed from the Greek 'kinema' meaning 'movement, motion'.
• Ibn al-Haytham is credited with being the first to treat geometry and kinematics as a unified concept.
• Kinematics differs from dynamics, which studies the effect of forces on bodies.
• Relativistic kinematics encompasses time dilation, length contraction, and the Lorentz transformation.