# Crackle (physics)

**Crackle** is the facetious name of a high-order derivative, and more specifically, the fifth derivative of the displacement.^{[1]} There is little consensus on what to call derivatives past the 4th derivative, jounce, due to there being few well-defined practical applications. The terms are, however, utilized within the fields of robotics and human motion.^{[2]}

## Notation

Crackle is given by the notation:

meaning crackle is equal to the 5th-order derivative of position vector over time, equal to the vector *s.*

The following equations are used for constant crackle:

where

- : constant crackle,
- : initial jounce,
- : final jounce,
- : initial jerk,
- : final jerk,
- : initial acceleration,
- : final acceleration,
- : initial velocity,
- : final velocity,
- : initial position,
- : final position,
- : time between initial and final states.

## See also

## References

- ↑ Uhlik, Christopher Richard (1990).
*Experiments in high-performance nonlinear and adaptive control of a two-link, flexible-drive-train manipulator*. Stanford University. p. 81. Retrieved 8 November 2015.Jerk is the technical term for the third derivative of position- snap, crackle, and pop correspond to the fourth, fifth, and sixth derivatives of position.

- ↑ Nagengast, Arne; Braun, Daniel; Wolpert, Daniel (26 June 2009). "Optimal Control Predicts Human Performance on Objects with Internal Degrees of Freedom".
*PLoS Comput Biol*.**5**(6). doi:10.1371/journal.pcbi.1000419. Retrieved 9 February 2016.

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