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In the study of [[mechanical network]]s in [[control theory]], an '''inerter''' is a two-terminal device in which the forces applied at the terminals are equal, opposite, and proportional to relative acceleration between the nodes. The generated strength satisfies the equation
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.
: <math>F=b(\dot{v}_2-\dot{v}_1)</math>,
for a suitable constant ''b''.


[[Malcolm C. Smith]], a [[control theory|control]] [[engineering]] professor at the [[University of Cambridge]], first introduced inerters in a 2002 paper.<ref>{{cite doi|10.1109/TAC.2002.803532}}</ref> However, a similar device was demonstrated in 1998 by Polish engineer Lucianus Lagiewka and used in an automobile bumper application. The principle and design are the same: a kinetic energy absorbing system that can be used as a bumper or vibration absorber.<ref>{{cite web| url= http://www.rexresearch.com/lagiewka/lagiewka.htm|title=Device for transforming kinetic energy}}</ref><ref>{{cite web| url=http://www.youtube.com/watch?feature=endscreen&NR=1&v=4_5oseSVUc4|title=Project EPAR}}</ref> The device was in the public knowledge since 1998. Smith extended the analogy between [[electrical network|electrical]] and [[mechanical network]]s (the [[mobility analogy]]). He observed that the analogy was incomplete, since it was missing a mechanical device playing the same role as an electrical [[capacitor]]. It was found that it is possible to construct such a device using gears.
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


==Applications==
Registered users will be able to choose between the following three rendering modes:
Shortly after its discovery, the inerter principle was used under the name of '''J-damper''' in the suspension systems of [[Formula 1]] [[racing car]]s. When tuned to the natural oscillation frequencies of the tires, the inerter reduced the mechanical load on the suspension. [[McLaren Mercedes]] began using a J-damper in early 2005, and [[Renault]] shortly thereafter.<ref>{{cite doi|10.1109/MCAS.2008.931738}}</ref>


J-dampers were at the center of the [[2007 Formula One espionage controversy]] which arose when Phil Mackereth left McLaren for Renault.
'''MathML'''
:<math forcemathmode="mathml">E=mc^2</math>


==Construction==
<!--'''PNG'''  (currently default in production)
A linear inerter can be constructed by meshing a [[flywheel]] with a [[rack gear]].  The pivot of the flywheel forms one terminal of the device, and the rack gear forms the other.
:<math forcemathmode="png">E=mc^2</math>


A rotational inerter can be constructed by meshing a flywheel with the ring gear of a [[differential (mechanical device)|differential]].  The side gears of the differential form the two terminals.
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


==References==
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].
{{Reflist}}


==External links==
==Demos==
* [http://www-control.eng.cam.ac.uk/~mcs/lecture_j.pdf The Inerter Concept and Its Applications], lecture notes
* [http://www.f1technical.net/features/10586 J-dampers in Formula 1]


[[Category:Control theory]]
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


{{automotive-tech-stub}}
 
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.
 
==Test pages ==
 
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]
 
*[[Inputtypes|Inputtypes (private Wikis only)]]
*[[Url2Image|Url2Image (private Wikis only)]]
==Bug reporting==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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