Stein's example - Revision history

en>SolidPhase: /* References */ split section into Notes and References

2014-12-21T17:50:06Z

References: split section into Notes and References

← Older revision		Revision as of 19:50, 21 December 2014
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en>Tomage: Replaceing the uppercase letter "i" with number "1"

2014-02-26T04:58:07Z

Replaceing the uppercase letter "i" with number "1"

← Older revision		Revision as of 06:58, 26 February 2014
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	~~In [[classical mechanics]], a '''central force''' on an object~~ is ~~a [[force~~ (~~physics~~)~~\|force]] whose magnitude only depends on the [[distance]] ''r'' of the object from the [[origin (mathematics)\|origin]]~~ and ~~is directed along the line joining them: <ref name="wolfram">~~		My name is Katlyn (30 years old) and my hobbies are Racquetball and Roller Derby.<br><br>Look into my page: [http://gestoresms.Ufms.br/?p=1%FFQuinton%FFexternal+nofollow%FFdarmowe+gry+casino+pobierz%FFexternal+nofollow%FFCrack+The+Sims+4%FFnofollow%FFCandy+Crush+Cheats%FFexternal+nofollow How to get free fifa 15 Coins]
	~~{{cite web~~
	~~\|url= http://scienceworld.wolfram~~.~~com/physics/CentralForce.html~~
	~~\|title= Central Force~~
	~~\|accessdate= 2008-08-18~~
	~~\|author= Eric W. Weisstein~~
	~~\|authorlink= Eric W. Weisstein~~
	~~\|year= 1996–2007~~
	~~\|work= ScienceWorld~~
	~~\|publisher= Wolfram Research~~
	}}
	<~~/ref~~>
	:<~~math~~> ~~\vec{F} = \mathbf{F}(\mathbf{r}) = F( \|\|\mathbf{r}\|\| ) \hat{\mathbf{r}} </math>~~
	where <math> \scriptstyle \vec{ \text{ F } } </math> is the force, '''F''' is a [[vector field\|vector valued force function]], ''F'' is a scalar valued force function, '''r''' is the [[position vector]], \|\|'''r'''\|\| is its length, and <math> \scriptstyle \hat{\mathbf{r}}</math> = '''r'''/\|\|'''r'''\|\| is the corresponding [[unit vector]].

	~~Equivalently, a force field is central if and only if it is [[spherically symmetric]].~~

	~~==Properties==~~
	~~A central force is a [[conservative field]], that is, it can always be expressed as the negative [[gradient]] of a [[potential]]:~~
	:~~<math> \mathbf{F}(\mathbf{r}) = - \mathbf{\nabla} V(\mathbf{r})\text{, where }V(\mathbf{r}) = \int_{\|\mathbf{r}\|}^{+\infin} F(r)\,\mathrm{d}r</math>~~
	~~(the upper bound of integration is arbitrary, as the potential is defined~~ [~~[up to]] an additive constant).~~

	~~In a conservative field, the total [[mechanical energy]] ([[kinetic energy\|kinetic]] and potential) is conserved:~~
	:~~<math>E = \frac{1}{2} m \|\mathbf{\dot{r}}\|^2 + V(\mathbf{r}) = \text{constant}<~~/~~math>~~
	~~(where '''ṙ''' denotes the [[derivative]] of '''r''' with respect to time, that is the [[velocity]]), and in a central force field, so is the [[angular momentum]]:~~
	~~:<math>\mathbf{L} = \mathbf{r} \times m\mathbf{\dot{r}} = \text{constant}<~~/~~math>~~
	~~because the [[torque]] exerted by the force is zero~~. As a consequence, the body moves on the plane perpendicular to the angular momentum vector and containing the origin, and obeys [[Kepler's laws of planetary motion\|Kepler's second law]]. (If the angular momentum is zero, the body moves along the line joining it with the origin.)

	~~As a consequence of being conservative, a central force field is irrotational, that is, its [[curl (mathematics)\|curl]] is zero, ''except at the origin'':~~
	~~:<math> \nabla\times\mathbf{F} (\mathbf{r}) = \mathbf{0}\text{.}<~~/~~math>~~

	~~==Examples=~~=
	~~[[Gravitational force]] and [[Coulomb force]] are two familiar examples with ''F''(''r'') being [[Inverse-square law\|proportional to~~ 1~~/''r''<sup>2</sup>]]. An object in such a force field with negative ''F'' (corresponding to an attractive force) obeys [[Kepler's laws of planetary motion]].~~

	The ~~force field of a spatial [[harmonic oscillator]] is central with ''F''(''r'') proportional~~ to ~~''r'' and negative.~~

	~~By [[Bertrand's theorem]], these two, ''F''(''r'') = −''k''/''r''<sup>2</sup> and ''F''(''r'') = −''kr'', are the only possible central force field with stable closed orbits.~~

	~~==See also==~~

	* [[Classical central-force problem]]

	~~==References==~~
	~~<references/>~~
	~~[[Category:Force]]~~
	~~[[Category:Classical mechanics]~~]

82.250.154.189: who is "surprised"? Keep factual , not opinions.

2013-12-13T00:35:28Z

who is "surprised"? Keep factual , not opinions.

← Older revision		Revision as of 02:35, 13 December 2013
Line 1:		Line 1:
	~~Herbal products are~~ an ~~excellent solution to be released from masculine impotence. Increase Testosterone Level - For~~ a ~~long time it was thought that certain unwanted symptoms were just part~~ of the ~~aging process~~ and ~~that there was nothing that could be done to treat~~ them. ~~Treatments or medications used for prostrate cancer reduce the manufacture of testosterone in the male testes and adrenal glands~~. ~~In many cases, erectile dysfunction is curable and indeed in recent years the markets have been flooded with pills that can help men achieve and maintain erections strong~~. ~~For most people, the major change in marriage comes with the birth of the first child~~. <br><br>~~A particular quite typical actual difficulty that produces erection dysfunction may be irregular pounds or carrying excess fat. This environment thus promotes~~ the ~~growth of the anaerobic bacteria. And for them~~, ~~the clear choice~~ is ~~to use herbal remedies. Cigarettes affect~~ the ~~amount of oxygen your body can absorb. Alcohol or drug abuse: Drugs such as antidepressants~~, ~~sedatives~~, and ~~antihypertensives have been known to contribute to impotence.~~ <br><br>~~Fortunately~~, ~~many patients regain potency 6 to 12 months after treatment~~. ~~Usually~~, ~~primary impotence~~ is ~~that type if the problem enrooted since the childhood even though the secondary~~ can be ~~began after some years~~ of ~~normal sexual acts. The five remaining species are gravely endangered~~, ~~in part due to~~ the ~~demand for their bones~~, ~~which are believed~~ to ~~treat arthritis~~, ~~and erroneously believed to reverse male impotence. The same holds true if you are already taking medications such as protease inhibitors. It hastens~~ the ~~growth of hair~~ and ~~stops the appearance of split ends.~~ <br><br>~~For easier assistance~~, ~~this sexual health disorder~~ is ~~mainly classified as venogenic, arteriogenic, neurogenic, mixed and psychogenic. The high selling price of~~ the ~~horns has brought about a sophisticated breed of poachers. These symptoms include lack of energy and motivation, fatigue, sleeping problems~~, ~~weight gain~~ and ~~increase in fat deposits in the abdomen, impotence, lack of interest~~ in ~~sex and other side effects. Often cause for pity, this problem can usually be handled if the actual problem is discovered. A person or couples health can definitely be~~ a ~~factor involving infertility~~, ~~however it~~ is ~~not usually one of~~ the ~~key factors.~~ <br><br>~~4T Plus capsule~~ is a ~~best recommended herbal supplement~~ to ~~treat male impotence in old age~~. ~~Ingesting medium chain fatty acids~~ is ~~rather valuable for people~~, ~~as they're quickly burnt by~~ the ~~human~~ body ~~filling~~ it with the ~~needed degree~~ of ~~stamina. Article Source: Ammons~~ is the ~~author of this article on Propecia Class Action~~. An ~~ability~~ to ~~maintain a penile erection requires a healthy & sound nervous system, healthy arteries in and near corpora cavernosa, smooth muscles & fibrous tissues in corpora cavernosa and abundant levels~~ of ~~nitric oxide~~. ~~This medication can benefit~~ a ~~number of mood disorders~~.<br><br>~~In case you adored this informative article along~~ with ~~you wish to obtain guidance about~~ [~~http://www.eiaculazione~~-~~precoce.info~~/ ~~supplements for harder erections~~] ~~i implore you to pay a visit to the site.~~		In [[classical mechanics]], a '''central force''' on an object is a [[force (physics)\|force]] whose magnitude only depends on the [[distance]] ''r'' of the object from the [[origin (mathematics)\|origin]] and is directed along the line joining them: <ref name="wolfram">
			{{cite web
			\|url= http://scienceworld.wolfram.com/physics/CentralForce.html
			\|title= Central Force
			\|accessdate= 2008-08-18
			\|author= Eric W. Weisstein
			\|authorlink= Eric W. Weisstein
			\|year= 1996–2007
			\|work= ScienceWorld
			\|publisher= Wolfram Research
			}}
			</ref>
			:<math> \vec{F} = \mathbf{F}(\mathbf{r}) = F( \|\|\mathbf{r}\|\| ) \hat{\mathbf{r}} </math>
			where <math> \scriptstyle \vec{ \text{ F } } </math> is the force, '''F''' is a [[vector field\|vector valued force function]], ''F'' is a scalar valued force function, '''r''' is the [[position vector]], \|\|'''r'''\|\| is its length, and <math> \scriptstyle \hat{\mathbf{r}}</math> = '''r'''/\|\|'''r'''\|\| is the corresponding [[unit vector]].

			Equivalently, a force field is central if and only if it is [[spherically symmetric]].

			==Properties==
			A central force is a [[conservative field]], that is, it can always be expressed as the negative [[gradient]] of a [[potential]]:
			:<math> \mathbf{F}(\mathbf{r}) = - \mathbf{\nabla} V(\mathbf{r})\text{, where }V(\mathbf{r}) = \int_{\|\mathbf{r}\|}^{+\infin} F(r)\,\mathrm{d}r</math>
			(the upper bound of integration is arbitrary, as the potential is defined [[up to]] an additive constant).

			In a conservative field, the total [[mechanical energy]] ([[kinetic energy\|kinetic]] and potential) is conserved:
			:<math>E = \frac{1}{2} m \|\mathbf{\dot{r}}\|^2 + V(\mathbf{r}) = \text{constant}</math>
			(where '''ṙ''' denotes the [[derivative]] of '''r''' with respect to time, that is the [[velocity]]), and in a central force field, so is the [[angular momentum]]:
			:<math>\mathbf{L} = \mathbf{r} \times m\mathbf{\dot{r}} = \text{constant}</math>
			because the [[torque]] exerted by the force is zero. As a consequence, the body moves on the plane perpendicular to the angular momentum vector and containing the origin, and obeys [[Kepler's laws of planetary motion\|Kepler's second law]]. (If the angular momentum is zero, the body moves along the line joining it with the origin.)

			As a consequence of being conservative, a central force field is irrotational, that is, its [[curl (mathematics)\|curl]] is zero, ''except at the origin'':
			:<math> \nabla\times\mathbf{F} (\mathbf{r}) = \mathbf{0}\text{.}</math>

			==Examples==
			[[Gravitational force]] and [[Coulomb force]] are two familiar examples with ''F''(''r'') being [[Inverse-square law\|proportional to 1/''r''<sup>2</sup>]]. An object in such a force field with negative ''F'' (corresponding to an attractive force) obeys [[Kepler's laws of planetary motion]].

			The force field of a spatial [[harmonic oscillator]] is central with ''F''(''r'') proportional to ''r'' and negative.

			By [[Bertrand's theorem]], these two, ''F''(''r'') = −''k''/''r''<sup>2</sup> and ''F''(''r'') = −''kr'', are the only possible central force field with stable closed orbits.

			==See also==

			* [[Classical central-force problem]]

			==References==
			<references/>
			[[Category:Force]]
			[[Category:Classical mechanics]]

en>Jimmy7430: /* An intuitive explanation */

2012-07-21T22:41:25Z

An intuitive explanation

New page

Herbal products are an excellent solution to be released from masculine impotence. Increase Testosterone Level - For a long time it was thought that certain unwanted symptoms were just part of the aging process and that there was nothing that could be done to treat them. Treatments or medications used for prostrate cancer reduce the manufacture of testosterone in the male testes and adrenal glands. In many cases, erectile dysfunction is curable and indeed in recent years the markets have been flooded with pills that can help men achieve and maintain erections strong. For most people, the major change in marriage comes with the birth of the first child. A particular quite typical actual difficulty that produces erection dysfunction may be irregular pounds or carrying excess fat. This environment thus promotes the growth of the anaerobic bacteria. And for them, the clear choice is to use herbal remedies. Cigarettes affect the amount of oxygen your body can absorb. Alcohol or drug abuse: Drugs such as antidepressants, sedatives, and antihypertensives have been known to contribute to impotence. Fortunately, many patients regain potency 6 to 12 months after treatment. Usually, primary impotence is that type if the problem enrooted since the childhood even though the secondary can be began after some years of normal sexual acts. The five remaining species are gravely endangered, in part due to the demand for their bones, which are believed to treat arthritis, and erroneously believed to reverse male impotence. The same holds true if you are already taking medications such as protease inhibitors. It hastens the growth of hair and stops the appearance of split ends. For easier assistance, this sexual health disorder is mainly classified as venogenic, arteriogenic, neurogenic, mixed and psychogenic. The high selling price of the horns has brought about a sophisticated breed of poachers. These symptoms include lack of energy and motivation, fatigue, sleeping problems, weight gain and increase in fat deposits in the abdomen, impotence, lack of interest in sex and other side effects. Often cause for pity, this problem can usually be handled if the actual problem is discovered. A person or couples health can definitely be a factor involving infertility, however it is not usually one of the key factors. 4T Plus capsule is a best recommended herbal supplement to treat male impotence in old age. Ingesting medium chain fatty acids is rather valuable for people, as they're quickly burnt by the human body filling it with the needed degree of stamina. Article Source: Ammons is the author of this article on Propecia Class Action. An ability to maintain a penile erection requires a healthy & sound nervous system, healthy arteries in and near corpora cavernosa, smooth muscles & fibrous tissues in corpora cavernosa and abundant levels of nitric oxide. This medication can benefit a number of mood disorders. In case you adored this informative article along with you wish to obtain guidance about [http://www.eiaculazione-precoce.info/ supplements for harder erections] i implore you to pay a visit to the site.