In physics, jounce, also known as snap, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is the second derivative of acceleration or the third derivative of velocity. Jounce is defined by any of the following equivalent expressions:
The following equations are used for constant jounce:
- is constant jounce,
- is initial jerk,
- is final jerk,
- is initial acceleration,
- is final acceleration,
- is initial velocity,
- is final velocity,
- is initial position,
- is final position,
- is time between initial and final states.
Jounce and the fifth and sixth derivatives of position as a function of time are "sometimes somewhat facetiously" referred to as snap, crackle, and pop respectively. However, time derivatives of position of higher order than four appear rarely.
- Thompson, Peter M. (5 May 2011). "Snap, Crackle, and Pop" (PDF). AIAA Info. Hawthorne, California: Systems Technology. p. 1. Retrieved 3 March 2017.
The common names for the first three derivatives are velocity, acceleration, and jerk. The not so common names for the next three derivatives are snap, crackle, and pop.
- Visser, Matt (31 March 2004). "Jerk, snap and the cosmological equation of state" (PDF). Classical and Quantum Gravity. 21 (11): 2603–2616. arXiv:gr-qc/0309109. Bibcode:2004CQGra..21.2603V. doi:10.1088/0264-9381/21/11/006. ISSN 0264-9381. Retrieved 17 May 2015.
Snap [the fourth time derivative] is also sometimes called jounce. The fifth and sixth time derivatives are sometimes somewhat facetiously referred to as crackle and pop.
- 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 2015-10-24.
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- Cosmography: cosmology without the Einstein equations, Matt Visser, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, 2004.