Jounce

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In physics, jounce 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; 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:

\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}

where

\vec j is jerk,
\vec a is acceleration,
\vec v is velocity,
\vec r is position,
\mathit{t} is time.

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".

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.

See also

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. arXiv:gr-qc/0309109. Bibcode 2004CQGra..21.2603V. doi:10.1088/0264-9381/21/11/006. 
  2. ^ 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. http://math.ucr.edu/home/baez/physics/General/jerk.html. Retrieved 2008-03-12. 

External links