Longitudinal mode - Revision history

en>RussBot: Robot: Editing intentional link to disambiguation page in hatnote per WP:INTDABLINK (explanation)

2014-09-22T12:56:18Z

Robot: Editing intentional link to disambiguation page in hatnote per WP:INTDABLINK (explanation)

← Older revision		Revision as of 14:56, 22 September 2014
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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~~.

	~~== For a system 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~~.

	== For a ~~rigid body ==~~
	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:

	~~<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>~~

	~~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~~>

	~~== References ==~~
	* 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]).~~

	*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

	=~~= Works Cited ==~~
	~~{{Reflist}}~~

	~~{{Physics-stub}}~~

	~~{{DEFAULTSORT:Konig's Theorem (Kinetics)}}~~
	~~[[Category:Mechanics]]~~
	~~[[Category:Physics theorems]~~]

en>NOrbeck: for air: n≈1.0002926

2013-04-20T04:23:25Z

for air: n≈1.0002926

← Older revision		Revision as of 06:23, 20 April 2013
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	~~Irwin Butts~~ is ~~what my wife enjoys to call me though I don't truly like being known as like~~ that. ~~Years~~ in the ~~past we moved~~ to ~~Puerto Rico~~ and ~~my family members enjoys it~~. ~~She is~~ a ~~librarian but she's always wanted her personal company.~~ The ~~thing she adores most~~ is body ~~developing~~ and ~~now she~~ is ~~trying~~ to ~~make money with it~~.<br><br>~~Also visit my web site~~ ... [http://~~nuvem~~.tk/~~altergalactica~~/~~AliceedMaurermy~~ http://~~nuvem~~.tk]		{{otheruses\|König's theorem (disambiguation)}}
			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.

			== For a system 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.

			== For a rigid body ==
			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:

			<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>

			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>

			== References ==
			* 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]).

			*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

			== Works Cited ==
			{{Reflist}}

			{{Physics-stub}}

			{{DEFAULTSORT:Konig's Theorem (Kinetics)}}
			[[Category:Mechanics]]
			[[Category:Physics theorems]]

en>ChrisGualtieri: TypoScan Project / General Fixes, typos fixed: , → , using AWB

2012-05-30T02:10:44Z

TypoScan Project / General Fixes, typos fixed: , → , using AWB

New page

Irwin Butts is what my wife enjoys to call me though I don't truly like being known as like that. Years in the past we moved to Puerto Rico and my family members enjoys it. She is a librarian but she's always wanted her personal company. The thing she adores most is body developing and now she is trying to make money with it.<br><br>Also visit my web site ... [http://nuvem.tk/altergalactica/AliceedMaurermy http://nuvem.tk]