Center of gravity

The center of mass system (CMS) is a reference system in which the center of gravity of the physical system under consideration rests in the origin of the coordinates . Many dynamic processes are particularly easy to describe in the center of gravity system.

From the definition of the priority system follows directly that in him the overall pulse of the masses involved (the sum of all pulse vectors ) at any time, before and after a shock - or responsive action, zero: ${\ displaystyle m_ {i}}$ ${\ displaystyle {\ vec {p}} _ {i}}$

${\ displaystyle \ sum _ {i} {\ vec {p}} _ {i} = {\ vec {0}}}$

The coordinates of the center of gravity S in the laboratory system - which in many practical cases can be viewed approximately as an inertial system - are ${\ displaystyle {\ vec {r}} _ {s} {}}$

${\ displaystyle {\ vec {r}} _ {s} = {\ frac {\ sum _ {i} m_ {i} {\ vec {r}} _ {i}} {\ sum _ {i} m_ { i}}}.}$

The transformation from one system to the other is in the classical case a Galilei transformation , in the relativistic case a Lorentz transformation .

In astronomy , the center of gravity of a multibody problem is called the barycentric system .

literature

• LD Landau, EM Lifschitz: Textbook of theoretical physics Volume 1: Mechanics , Akademie Verlag Berlin 1970
• Dieter Meschede: Gerthsen Physik , Springer, 24th edition 2010, ISBN 978-3-642-12893-6
• Andreas Guthmann: Introduction to celestial mechanics and ephemeris calculation , Spectrum Academic Publishing House, 2nd edition 2000, ISBN 3-8274-0574-2