In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. The higher-order derivatives are less common than the first three;[1][2] thus their names are not as standardized, though the concept of a minimum snap trajectory has been used in robotics and is implemented in MATLAB.[3]
The fourth derivative is referred to as snap, leading the fifth and sixth derivatives to be "sometimes somewhat facetiously"[4] called crackle and pop, inspired by the Rice Krispies mascots Snap, Crackle, and Pop.[5] The fourth derivative is also called jounce.[4]
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