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]


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.

See also


  1. 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.
  2. 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.
This article is issued from Wikipedia - version of the 11/23/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.