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In [[physics]], '''jounce''' or '''snap'''<ref>https://info.aiaa.org/Regions/Western/Orange_County/Newsletters/AIAAOC_SnapCracklePop_docx.pdf</ref> is the fourth [[derivative]] of the [[Position (vector)|position vector]] with respect to [[time]], with the first, second, and third derivatives being [[velocity]], [[acceleration]], and [[jerk (physics)|jerk]], respectively; in other words, the jounce is the rate of change of the jerk with respect to time. Jounce is defined by any of the following equivalent expressions:
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:<math>\vec s =\frac {d \vec j} {dt}=\frac {d^2 \vec a} {dt^2}=\frac {d^3 \vec v} {dt^3}=\frac {d^4 \vec r} {dt^4}</math>
 
the following equation is used for constant jounce.
* <math>j = j. + st </math>
* <math>a = a. + j.t + \frac{1}{2}st^2 </math>
* <math>v = v. + a.t + \frac{1}{2}j.t^2 + \frac{1}{6}st^3 </math>
* <math>S = v.t + \frac{1}{2}a.t^2 + \frac{1}{6}j.t^3 + \frac{1}{24}st^4 </math>
where
:<math>\vec s</math> is constant jounce,
:<math>\vec j.</math> is initial jerk,
:<math>\vec j</math> is final jerk,
:<math>\vec a.</math> is initial acceleration,
:<math>\vec a</math> is final acceleration,
:<math>\vec v.</math> is initial velocity,
:<math>\vec v</math> is final velocity,
:<math>\vec S</math> is distance or displacement
:<math>\vec r</math> is position,
:<math>\mathit{t}</math> is time.
 
The notation <math>\vec s</math> (used in <ref name=MVisser1 />) is not to be confused with the [[displacement vector]] commonly denoted similarly. Currently, there are no well-accepted designations for the derivatives of jounce. The fourth, fifth and sixth derivatives of position as a function of time are "sometimes somewhat facetiously"<ref name=MVisser1>
{{cite journal
  | last = Visser | first = Matt
  | authorlink = Matt Visser
  | title = Jerk, Snap, and the Cosmological Equation of State
  | journal = Classical and Quantum Gravity
  | volume = 21 | issue = 11 | pages = 2603–2616
  | date = 2004-07-24
  | arxiv = gr-qc/0309109
  | doi = 10.1088/0264-9381/21/11/006
  | bibcode = 2004CQGra..21.2603V }}</ref><ref name="PhysicsFAQ">{{cite web
  | last = Gragert
  | first = Stephanie
  | title = What is the term used for the third derivative of position?
   | url = http://math.ucr.edu/home/baez/physics/General/jerk.html
   | publisher = Math Dept., [[University of California, Riverside]]
  | work = Usenet Physics and Relativity FAQ
  | date = November 1998
  | accessdate = 2008-03-12
}}</ref> referred to as [[Snap, Crackle, and Pop|"Snap", "Crackle", and "Pop"]] respectively.
 
The dimensions of jounce are distance per (time to the power of 4). In [[SI units]], this is "metres per quartic second", "metres per second per second per second per second", m/s<sup>4</sup>, m &middot; s<sup>-4</sup>, or 100 [[Gal (unit)|Gal]] per second squared in [[CGS]] units.
 
==References==
{{Reflist}}
 
== External links ==
{{Wiktionary}}
*[http://arxiv.org/pdf/gr-qc/0411131 ''Cosmography: cosmology without the Einstein equations''], Matt Visser, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, 2004.
*[http://math.ucr.edu/home/baez/physics/General/jerk.html ''What is the term used for the third derivative of position?'']
 
{{Kinematics}}
 
[[Category:Physical quantities]]
[[Category:Time]]
[[Category:Acceleration]]
 
{{classicalmechanics-stub}}

Latest revision as of 19:24, 12 March 2014

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