Triangle-free graph - Revision history

en>Rjwilmsi: /* References */Added 1 doi to a journal cite using AWB (10210)

2014-05-24T10:32:03Z

References: Added 1 doi to a journal cite using AWB (10210)

← Older revision		Revision as of 12:32, 24 May 2014
Line 1:		Line 1:
	A mechanical system is '''rheonomous''' if its equations of [[Constraint (classical mechanics)\|constraints]] contain the time as an explicit variable.<ref name=Herb1980>{{cite book \|last=Goldstein \|first=Herbert \|authorlink=Herbert Goldstein \|title=Classical Mechanics \|year=1980 \|location=United States of America \|publisher=Addison Wesley \|edition=2nd \|isbn=0-201-02918-9 \|page=12 \|quote=Constraints are further classified according as the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous).}}</ref><ref name=spiegel1994>{{cite book \|last=Spiegel \|first=Murray R. \|title=Theory and Problems of THEORETICAL MECHANICS with an Introduction to Lagrange's Equations and Hamiltonian Theory \|year=1994 \|series=Schaum's Outline Series \|publisher=McGraw Hill \|isbn=0-07-060232-8 \|page=283 \|quote=In many mechanical systems of importance the time ''t'' does not enter explicitly in the equations (''2'') or (''3''). Such systems are sometimes called ''scleronomic''. In others, ~~as for example those involving moving constraints, the time '~~'t~~'' does enter explicitly. Such systems are~~ called ~~''rheonomic''.}}</ref> Such constraints are called '''rheonomic constraints'''~~. ~~The opposite of rheonomous~~ is ~~[[scleronomous]]~~.~~<ref name=Herb1980/><ref name=spiegel1994/>~~		Nice to satisfy you, my title is Figures Held although I don't really like being called like that. North Dakota is her beginning place but she will have to move one working day or an additional. Hiring is his profession. Playing baseball is the pastime he will never stop doing.<br><br>Also visit my website ... at home std test, [http://fastrolls.com/index.php?do=/profile-72113/info/ visit the following page],

	~~==Example: simple 2D pendulum==~~
	~~[[File:SimplePendulum01.JPG\|frame\|right\|A simple pendulum]]~~
	~~As shown at right, a simple [[pendulum]]~~ is ~~a system composed of a weight and a string~~. ~~The string~~ is ~~attached at~~ the ~~top end to a pivot and at the bottom end to a weight~~. ~~Being inextensible, the string has a constant length. Therefore this system is scleronomous; it obeys the scleronomic constraint~~
	: <~~math~~> ~~\sqrt{x^2+y^2} - L=0\,\!~~<~~/math~~>,
	~~where <math>(x,\ y)\,\!</math> is the position of the weight and <math>L\,\!</math> the length of the string~~.

	~~[[File:Pendulum02~~.~~JPG\|frame\|right\|A simple pendulum with oscillating pivot point]]~~
	~~The situation changes if the pivot point is moving~~, ~~e.g. undergoing a~~ [~~[simple harmonic motion]]~~
	:~~<math>x_t=x_0\cos\omega t\,\!<~~/~~math>,~~
	~~where <math>x_0\,\!<~~/~~math> is the amplitude, <math>\omega\,\!<~~/~~math> the angular frequency, and <math>t\,\!<~~/~~math> time.~~

	Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore this system is rheonomous; it obeys the rheonomic constraint
	~~:<math> \sqrt{(x~~ - ~~x_0\cos\omega t)^2+y^2} - L=0\,\!<~~/~~math>.~~

	~~==See also==~~
	*[[Lagrangian mechanics]]
	*[[Holonomic constraints]]

	~~==References==~~
	~~<references~~ />

	~~[[Category:Mechanics]]~~
	~~[[Category:Classical mechanics]]~~
	~~[[Category:Lagrangian mechanics]~~]

14.139.56.184: /* Independence number and Ramsey theory */

2013-11-01T17:32:56Z

Independence number and Ramsey theory

← Older revision		Revision as of 19:32, 1 November 2013
Line 1:		Line 1:
	~~Nice~~ to ~~meet you~~, ~~I am Marvella Shryock~~. ~~I am~~ a ~~meter reader~~. ~~To gather cash~~ is a ~~factor that I'm totally addicted~~ to. ~~California~~ is ~~our birth location.~~<br><br>~~my web page;~~ [~~http~~:~~//www~~.~~adosphere~~.~~com~~/~~member~~/~~28512~~/~~blog~~/~~view~~/~~66112~~/ ~~std home test~~]		A mechanical system is '''rheonomous''' if its equations of [[Constraint (classical mechanics)\|constraints]] contain the time as an explicit variable.<ref name=Herb1980>{{cite book \|last=Goldstein \|first=Herbert \|authorlink=Herbert Goldstein \|title=Classical Mechanics \|year=1980 \|location=United States of America \|publisher=Addison Wesley \|edition=2nd \|isbn=0-201-02918-9 \|page=12 \|quote=Constraints are further classified according as the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous).}}</ref><ref name=spiegel1994>{{cite book \|last=Spiegel \|first=Murray R. \|title=Theory and Problems of THEORETICAL MECHANICS with an Introduction to Lagrange's Equations and Hamiltonian Theory \|year=1994 \|series=Schaum's Outline Series \|publisher=McGraw Hill \|isbn=0-07-060232-8 \|page=283 \|quote=In many mechanical systems of importance the time ''t'' does not enter explicitly in the equations (''2'') or (''3''). Such systems are sometimes called ''scleronomic''. In others, as for example those involving moving constraints, the time ''t'' does enter explicitly. Such systems are called ''rheonomic''.}}</ref> Such constraints are called '''rheonomic constraints'''. The opposite of rheonomous is [[scleronomous]].<ref name=Herb1980/><ref name=spiegel1994/>

			==Example: simple 2D pendulum==
			[[File:SimplePendulum01.JPG\|frame\|right\|A simple pendulum]]
			As shown at right, a simple [[pendulum]] is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length. Therefore this system is scleronomous; it obeys the scleronomic constraint
			: <math> \sqrt{x^2+y^2} - L=0\,\!</math>,
			where <math>(x,\ y)\,\!</math> is the position of the weight and <math>L\,\!</math> the length of the string.

			[[File:Pendulum02.JPG\|frame\|right\|A simple pendulum with oscillating pivot point]]
			The situation changes if the pivot point is moving, e.g. undergoing a [[simple harmonic motion]]
			:<math>x_t=x_0\cos\omega t\,\!</math>,
			where <math>x_0\,\!</math> is the amplitude, <math>\omega\,\!</math> the angular frequency, and <math>t\,\!</math> time.

			Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore this system is rheonomous; it obeys the rheonomic constraint
			:<math> \sqrt{(x - x_0\cos\omega t)^2+y^2} - L=0\,\!</math>.

			==See also==
			*[[Lagrangian mechanics]]
			*[[Holonomic constraints]]

			==References==
			<references />

			[[Category:Mechanics]]
			[[Category:Classical mechanics]]
			[[Category:Lagrangian mechanics]]

en>ClueBot NG: Reverting possible vandalism by 99.229.202.236 to version by 131.96.49.182. False positive? Report it. Thanks, ClueBot NG. (806764) (Bot)

2012-01-10T23:27:50Z

Reverting possible vandalism by 99.229.202.236 to version by 131.96.49.182. False positive? Report it. Thanks, ClueBot NG. (806764) (Bot)

New page

Nice to meet you, I am Marvella Shryock. I am a meter reader. To gather cash is a factor that I'm totally addicted to. California is our birth location.<br><br>my web page; [http://www.adosphere.com/member/28512/blog/view/66112/ std home test]