8.4: Higher Derivatives
( \newcommand{\kernel}{\mathrm{null}\,}\)
Occasionally one may have a use for higher derivatives of position with respect to time. The time derivative of acceleration is called jerk, and the time derivative of jerk is called jounce. One published paper 1 whimsically named the fourth, fifth, and sixth derivatives of x "snap", "crackle", and "pop" after the cartoon characters on boxes of Rice Krispies ® breakfast cereal.
We will seldom, if ever, have need of these higher-order derivatives of x for this course, but for reference, they are summarized in Table 8.4.1.
Table 8.4.1. Time derivatives of position.
Derivative | Symbol | Name |
0 | x | position |
1 | dx/dt | velocity |
2 | d2x/dt2 | acceleration |
3 | d3x/dt3 | jerk |
4 | d4x/dt4 | jounce, snap |
5 | d5x/dt5 | crackle |
6 | d6x/dt6 | pop |
1. Visser, Matt. Jerk, Snap, and the Cosmological Equation of State. Classical and Quantum Gravity, 21 (11): 2603-2616.