Konig's theorem, also called Konig's decomposition, is a relation in kinematics derived by Johann Samuel Konig that separates a system of particles' total kinetic energy and angular momentum into a part carried by the motion of the system's center of mass and a part carried by motion relative to that center of mass. It's a standard tool for analyzing rotating rigid bodies and multi-particle systems, since the translational and internal contributions to energy and angular momentum can be worked out separately and then combined.
Facts
StatementThe 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 angular momentum of the system likewise splits into the angular momentum of the center of mass and the angular momentum of the particles relative to the center of mass. 1 Sources
1. Konig's theorem (kinetics), Wikipedia
Second part of König's theorem
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.
References
Samuel Konig (Sam. Koenigio): De universali principio aequilibrii & motus, in vi viva reperto, deque nexu inter vim vivam & actionem, utriusque minimo, dissertatio, Nova acta eruditorum (1751) 125-135, 162-176
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