Particle in a ring - Revision history

en>Ost316: Disambiguate Buckyballs to Buckyball (molecule) using popups; formatting: 5x whitespace, heading-style (using Advisor.js)

2014-10-08T18:20:48Z

Disambiguate Buckyballs to Buckyball (molecule) using popups; formatting: 5x whitespace, heading-style (using Advisor.js)

← Older revision		Revision as of 20:20, 8 October 2014
Line 1:		Line 1:
	~~{{about\|\|pain and/or loss of range of motion of a joint\|joint stiffness\|the term regarding the stability of a differential equation\|stiff equation}}~~		Wilber Berryhill is the name his parents gave him and he totally digs that title. One of the extremely best things in the globe for him is performing ballet and he'll be beginning something else alongside with it. Distributing production is how he makes a living. I've always cherished residing in Kentucky but now I'm contemplating other choices.<br><br>Stop by my website - [http://beauty.thuvienbao.com/profile.php?u=MaBrandenb free psychic readings]
	~~{{redirect\|Flexibility}}~~
	~~[[File:Beam bending.svg\|thumb\|right]]~~
	~~'''Stiffness''' is the rigidity of an object — the extent to which it resists [[deformation (mechanics)\|deformation]] in response to an applied [[force]].<ref>{{cite journal~~
	~~\| title = Stiffness--an unknown world of mechanical science?~~
	~~\| journal = Injury~~
	~~\| author = Baumgart F.~~
	~~\| year = 2000~~
	~~\| volume = 31~~
	~~\| publisher = Elsevier~~
	~~\| quote = “Stiffness” = “Load” divided by “Deformation”~~
	~~\| url = http://www.sciencedirect.com/science/article/pii/S0020138300800406~~
	~~\| accessdate = 2012-05-04~~
	~~\| doi=10.1016/S0020-1383(00)80040-6}}</ref> The complementary concept is '''flexibility''' or pliability: the more flexible an object~~ is, the ~~less stiff it is.<ref>{{citation \|page=126 \|chapter=Stiffness~~ and ~~flexibility \|~~title~~=200 science investigations for young students \|author=Martin Wenham \|year=2001 \|isbn=978-0-7619-6349-3}}</ref>~~

	~~==Calculations==~~
	~~'''The stiffness''', ''k'', '''of a body''' is a measure of the resistance offered by an elastic body to deformation~~. ~~For an elastic body with a single [[Degrees~~ of ~~freedom (mechanics)\|degree of freedom]] (for example, stretching or compression of a rod),~~ the ~~stiffness is defined as~~

	~~:<math>k=\frac {F} {\delta} </math>~~

	~~where,~~

	~~:''F'' is the force applied on the body~~
	~~:δ is~~ the ~~[[displacement field (mechanics)\|displacement]] produced by the force along the same degree of freedom (~~for ~~instance, the change in length of a stretched spring)~~

	~~In the [[International System of Units]], stiffness is typically measured in [[Newton (unit)\|newton]]s per metre.~~
	~~In Imperial units, stiffness is typically measured in [[Pound (force)\|pound]]s(lbs) per inch.~~

	~~Generally speaking, [[Deflection (engineering)\|deflections]] (or motions) of an infinitesimal element (which~~ is viewed as a point) in an elastic body can occur along multiple [[Degrees of freedom (mechanics)\|degrees of freedom]] (maximum of six DOF at a point). For example, a point on a horizontal [[Euler–Bernoulli beam equation\|beam]] can undergo both a vertical [[Displacement (vector)\|displacement]] and ~~a rotation relative to its undeformed axis. When there are M degrees of freedom a M x M [[Matrix (mathematics)\|matrix]] must~~ be used to describe the stiffness at the point. The diagonal terms in the matrix are the direct-related stiffnesses (or simply stiffnesses) along the same degree of freedom and the off-diagonal terms are the coupling stiffnesses between two different degrees of freedom (either at the same or different points) or the same degree of freedom at two different points. In industry, the term '''influence coefficient''' is sometimes used to refer to the coupling stiffness.

	~~It is noted that for a body~~ with multiple DOF, the equation above generally does not apply since the applied force generates not only the deflection along its own direction (or degree of freedom), but also those along other directions.

	~~For a body with multiple DOF, in order to calculate a particular direct-related stiffness (the diagonal terms), the corresponding DOF~~ is ~~left free while the remaining should be constrained. Under such~~ a ~~condition, the above equation can be used to obtain the direct-related stiffness for the degree of freedom which is unconstrained~~. ~~The ratios between the reaction forces (or moments) and the produced deflection are the coupling stiffnesses.~~

	~~== Compliance ==~~

	~~The [[Multiplicative inverse\|inverse]] of stiffness is~~ ''compliance'', typically measured in units of metres per newton. In rheology it may be defined as the ratio of strain to stress,<ref>V. GOPALAKRISHNAN and CHARLES F. ZUKOSKI; "Delayed flow in thermo-reversible colloidal gels"; Journal of Rheology; Society of Rheology, U.S.A.; July/August 2007; 51 (4): pp. 623–644.<~~/ref~~> ~~and so take the units of reciprocal stress, ''e.g''. 1/[[pascal (unit)\|Pa]].~~

	~~== Rotational stiffness ==~~<~~!-- [[Torsional rigidity]] redirects here --~~>

	~~A body may also have a rotational stiffness, ''k'', given~~ by

	~~:<math>k=\frac {M} {\theta} </math>~~

	~~where~~
	~~: ''M'' is the applied [[moment (physics)\|moment]]~~
	~~: ''θ'' is the rotation~~

	~~In the SI system, rotational stiffness is typically measured in [[newton~~-~~metre]]s per~~ [~~[radian]].~~

	~~In the SAE system, rotational stiffness is typically measured in inch-[[Pound (force)\|pound]]s per [[degree (angle)\|degree]].~~

	~~Further measures of stiffness are derived on a similar basis, including:~~

	* shear stiffness - ratio of applied [[shear stress\|shear]] force to shear deformation
	* torsional stiffness - ratio of applied [[torsion (mechanics)\|torsion]] moment to angle of twist

	~~== Relationship to elasticity ==~~
	In general, [[elastic modulus]] is not the same as stiffness. Elastic modulus is a property of the constituent material; stiffness is a property of a structure. That is, the modulus is an [[intensive and extensive properties\|intensive property]] of the material; stiffness, on the other hand, is an [[intensive and extensive properties\|extensive property]] of the solid body dependent on the material ''and'' the shape and boundary conditions. For example, for an element in [[tension (mechanics)\|tension]] or [[compression (physical)\|compression]], the axial stiffness is

	:~~<math>k=\frac {AE} {L} <~~/~~math>~~

	~~where~~
	~~:''A'' is the cross-sectional area,~~
	~~:''E'' is the (tensile) elastic modulus (or [[Young's modulus]]),~~
	~~:''L'' is the length of the element.~~

	~~Similarly, the rotational stiffness is~~

	~~:<math>k=\frac {nGI} {L} <~~/~~math>~~

	~~where~~
	~~:"I" is the polar moment of inertia,~~
	~~:"n" is an integer depending on the boundary condition (=4 for fixed ends)~~
	~~:"G" is the rigidity modulus of the material~~

	~~For the special case of unconstrained uniaxial tension or compression, [[Young's modulus]] ''can'' be thought of as a measure of the stiffness of a material~~.

	~~== Use in engineering ==~~
	~~The stiffness of a structure is of principal importance in many engineering applications, so the [[modulus of elasticity]] is often one of the primary properties considered when selecting a material~~. ~~A high modulus of elasticity is sought when [[Deflection (engineering)\|deflection]] is undesirable, while a low modulus of elasticity is required when flexibility is needed~~.

	=~~= See also ==~~
	*[[Elasticity (physics)]]
	*[[Elastic modulus]]
	*[[Mechanical impedance]]
	*[[Hardness]]
	*[[Hooke's law]]
	*[[Moment of inertia]]
	*[[Stiffness (mathematics)]]
	*[[Young's modulus]]
	*[[Compliant mechanism]]

	~~== References ==~~
	~~{{Reflist}}~~

	~~[[Category:Physical quantities]]~~
	~~[[Category:Continuum mechanics]]~~
	~~[[Category:Structural analysis]~~]

143.239.9.1: /* Wave function */

2013-12-03T20:51:42Z

Wave function

Show changes

24.232.224.70: Fixed momentum operator representation in the position basis

2012-03-31T23:54:05Z

Fixed momentum operator representation in the position basis

New page

Most individuals have this habit of doing all stuff by themselves, irrespective of how critical or simple they are! These folks won't let others interfere inside their affairs. While this stance will function inside alternative regions of lifetime, it's not how to answer when you want to fix a Windows registry. There are some jobs such as removing spywares, virus and obsolete registry entries, that are best left to pro softwares. In this article I usually tell we why it is important to fix Windows registry NOW! You need to understand some simple and cheap methods which can resolve the issue of the computer plus speed it up. The earlier you fix it, the less damage your computer gets. I usually tell about several valuable techniques that can enable we to speed up you computer. The error is basically a outcome of issue with Windows Installer package. The Windows Installer is a tool employed to install, uninstall and repair the most programs on your computer. Let you discuss a limited things that helped a lot of folks whom facing the synonymous matter. Fixing tcpip.sys blue screen is simple to do with registry repair software.Trying to fix windows blue screen error on your is tricky because if you remove or damage the registry it may result serious damage to your computer. The registry must be cleaned and all erroneous and incomplete information removed to stop blue screen mistakes from occurring.The advantage of registry repair software is not limited to only getting rid of the blue screen on startup.You would be surprised at the better and more improved speed and performance of the computer program following registry cleaning is done. Registry cleaning can definitely develop your computer's working abilities, incredibly when we choose a certain registry repair software that is very efficient. Many [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities] s enable you to download their product for free, thus you can scan the computer yourself. That method you are able to see how numerous mistakes it finds, where it finds them, and how it may fix them. A great registry cleaner might remove a registry issues, plus optimize plus speed up your PC, with small effort on the piece. If you think that there are issues with the d3d9.dll file, then you need to substitute it with a brand-new functioning file. This is done by performing a series of steps and you are able to start by obtaining "d3d9.zip" within the host. Next you must unzip the "d3d9.dll" file found on the difficult drive of the computer. Proceed by locating "C:\Windows\System32" and then acquiring the existing "d3d9.dll" on your PC. When found, rename the file "d3d9.dll to d3d9BACKUP.dll" plus then copy-paste this new file to "C:\Windows\System32". After that, hit "Start" followed by "Run" or search "Run" on Windows Vista & 7. As soon because a box shows up, type "cmd". A black screen may then appear and you have to sort "regsvr32d3d9.dll" and then click "Enter". This procedure usually help you to substitute the aged file with the fresh copy. Maybe you may be asking why these windows XP error messages appear. Well, for we to be able to recognize the fix, you need to initially know where those mistakes come from. There is this software called registry. A registry is software which stores everything on your PC from a normal configuration, setting, info, plus logs of escapades from installing to UN-installing, saving to deleting, and a lot more alterations you do in a system pass through it and gets 'tagged' plus saved as a simple file for healing reasons. Imagine it because a big recorder, a registrar, of all the records inside the PC. Registry cleaners have been designed to fix all of the broken files inside your system, allowing a computer to read any file it wants, whenever it wants. They function by scanning through the registry plus checking every registry file. If the cleaner sees it is corrupt, then it can replace it automatically.