König's theorem (kinetics)

In kinetics, König's theorem or König's decomposition is a mathematical relation derived by Johann Samuel König that assists with the calculation of kinetic energy of bodies and systems of particles.

The theorem expresses the kinetic energy of a system of particles in terms of the velocities of the individual particles.

Specifically, it states that the kinetic energy of a system of particles is the sum of the kinetic energy associated to the movement of the center of mass and the kinetic energy associated to the movement of the particles relative to the center of mass.

The theorem can also be applied to rigid bodies, stating that the kinetic energy T of a rigid body, as viewed by an observer fixed in some inertial reference frame N, can be written as:

${\displaystyle ^{N}T={\frac {1}{2}}m\cdot {^{N}\mathbf {\bar {v}} }\cdot {^{N}\mathbf {\bar {v}} }+{\frac {1}{2}}{^{N}\!\mathbf {\bar {H}} }\cdot ^{N}{\!\!\mathbf {\omega } }^{R}}$

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