The rate of change of acceleration is the jerk and we experience that everyday when starting up our cars or braking when the lights turn red.

Snap, crackle and pop are terms, based on the Rice Krispies mascots, used for the fourth, fifth and sixth time derivatives of position. The first derivative of position with respect to time is velocity, the second is acceleration, and the third is jerk. The term snap will be used throughout this paper to denote the fourth derivative of displacement with respect to time. Another name for this fourth derivative is jounce. The fifth and sixth derivatives with respect to time are referred to as crackle and pop respectively.

The rate of change of jerk, the fourth derivative of displacement with respect to time, is called the snap. Positioning spacecraft requires the calculation of snap.

Snap too may vary with time. The fifth derivative is called the crackle and the sixth derivative is called the pop but these and higher derivatives have not – yet – found practical application.

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Tags: crackle, pop, snap