abstract

In physics, Koenig theorem is a basic theorem in the kinematics of particle systems.

In graph theory, Koenig theorem is a theorem about the relationship between bipartite graph matching and point covering.

Literally, the total kinetic energy of the particle system is equal to the kinetic energy of the center of mass when all the masses are concentrated in the center of mass plus the kinetic energy of each particle moving in the translation coordinate system relative to the center of mass.

mathematical expression

T =1/2 (∑ Mi) * VC 2+1/2 ∑ (mi * vi 2)//lowercase letters are subscripts, for example, in mi, I is the subscript of m.

Where: t is the kinetic energy of the particle system, Mi is the mass of the ith particle in the particle system, Vc is the velocity of the center of mass, and Vi is the velocity of the ith particle relative to the center of mass.

Koenig theorem shows that the kinetic energy of a particle system is equal to the sum of the kinetic energy of the center of mass and the kinetic energy of the particle system to the motion of the center of mass.

Attachment: derivation

ek =σ 1/2 mivi^2

= σ 1/2mi (v relative +VC) 2

=σ 1/2 mivc 2+σmivcv relative+σ 1/2 mivv relative 2

= σ 1/2 mivc 2+Vcσ (relative miv)+σ1/2miv2.

Because c is the center of mass and σ (miv relative) =0, it is proved that.

The above Vi, V and Vc are all vectors.

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