Crackle is the facetious name of a high-order derivative, and more specifically, the fifth derivative of the displacement. 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.
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:
- : 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.
- 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.