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| {{otheruses|König's theorem (disambiguation)}}
| | Hi there. Allow me begin by introducing the author, her name is Myrtle Cleary. California is exactly where I've usually been residing and I love each day residing here. For many years he's been operating as a receptionist. To collect badges is what her family and her enjoy.<br><br>my weblog - [http://javly.com/?p=56362 at home std testing] |
| In [[kinetics (physics)|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.
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| == For a system of particles ==
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| The theorem expresses the kinetic energy of a system of particles in terms of the velocities of the individual particles.
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| 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.
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| == For a rigid body ==
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| 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 [[Frame_of_reference|reference frame]] N, can be written as:
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| <math>^{N}T = \frac{1}{2} {^N\mathbf{\bar{v}}} \cdot {^N\mathbf{\bar{v}}} + \frac{1}{2} {^N\!\mathbf{\bar{H}}} \cdot ^{N}{\!\!\mathbf{\omega}}^R </math>
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| where <math>{^N\mathbf{\bar{v}}}</math> is the velocity of the center of mass of the rigid body, as viewed by an observer fixed in an inertial frame N; <math>{^N\!\mathbf{\bar{H}}}</math> is the [[angular momentum]] of the rigid body about the center of mass, also taken in the inertial frame N; and <math>^{N}{\!\!\mathbf{\omega}}^R</math> is the angular velocity of the rigid body R relative to the inertial frame N. <ref>{{cite book |last=Rao |first=Anil V. |title=Dynamics of Particles and Rigid Bodies: A Systematic Approach |publisher=Cambridge University Press |page=421}}</ref>
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| == References ==
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| * Samuel König (Sam. Koenigio): ''De universali principio æquilibrii & motus, in vi viva reperto, deque nexu inter vim vivam & actionem, utriusque minimo, dissertatio'', [http://www.izwt.uni-wuppertal.de/repertorium/MS/NAE_1751.html Nova acta eruditorum (1751) 125-135, 162-176] ([http://web.archive.org/web/20110719112147/http://www.izwt.uni-wuppertal.de/repertorium/MS/NAE_1751.html Archived]).
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| *Paul A. Tipler and Gene Mosca (2003), Physics for Scientists and Engineers (Paper) : Volume 1A: Mechanics (Physics for Scientists and Engineers), W. H. Freeman Ed., ISBN 0-7167-0900-7
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| == Works Cited == | |
| {{Reflist}}
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| {{Physics-stub}}
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| {{DEFAULTSORT:Konig's Theorem (Kinetics)}}
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| [[Category:Mechanics]]
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| [[Category:Physics theorems]]
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Hi there. Allow me begin by introducing the author, her name is Myrtle Cleary. California is exactly where I've usually been residing and I love each day residing here. For many years he's been operating as a receptionist. To collect badges is what her family and her enjoy.
my weblog - at home std testing