Crackle (physics)

In physics, jounce or snap is the fourth derivative of the position vector with respect to time, with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively; hence, the jounce is the rate of change of the jerk with respect to time. Jounce is defined by any of the following equivalent expressions:

Graphical Model of Jounce
\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}

The following equations are used for constant jounce:

\vec j = \vec j_0 + \vec s \,t
\vec a = \vec a_0 + \vec j_0 \,t + \frac{1}{2} \vec s \,t^2
\vec v = \vec v_0 + \vec a_0 \,t + \frac{1}{2} \vec j_0 \,t^2 + \frac{1}{6} \vec s \,t^3
\vec r = \vec r_0 + \vec v_0 \,t + \frac{1}{2} \vec a_0 \,t^2 + \frac{1}{6} \vec j_0 \,t^3 + \frac{1}{24} \vec s \,t^4

where

\vec s : constant jounce,
\vec j_0 : initial jerk,
\vec j : final jerk,
\vec a_0 : initial acceleration,
\vec a : final acceleration,
\vec v_0 : initial velocity,
\vec v : final velocity,
\vec r_0 : initial position,
\vec r : final position,
t : time between initial and final states.

The notation \vec s (used in [1]) 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"[1][2] referred to as Snap, Crackle and Pop respectively. Because higher-order derivatives are not commonly useful, there has been no consensus among physicists on the proper names for derivatives above jounce.[2] Despite this, physicists have proposed other names such as "Lock", "Drop", "Shot" and "Put" for higher-ordered derivatives.

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/s4, m · s−4, or 100 Gal per second squared in CGS units. This pattern continues for higher order derivatives, with the 5th being m/s5.

References

  1. ^ a b Visser, Matt (2004-07-24). "Jerk, Snap, and the Cosmological Equation of State". Classical and Quantum Gravity 21 (11): 2603–2616. Bibcode:2004CQGra..21.2603V. arXiv:gr-qc/0309109. doi:10.1088/0264-9381/21/11/006. 
  2. ^ a b Gragert, Stephanie (November 1998). "What is the term used for the third derivative of position?". Usenet Physics and Relativity FAQ. Math Dept., University of California, Riverside. Retrieved 2008-03-12. 

External links

  • Cosmography: cosmology without the Einstein equations, Matt Visser, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, 2004.
  • What is the term used for the third derivative of position?


This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.