Fourth, fifth, and sixth derivatives of position

Time-derivatives of position

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]

  1. ^ Eager, David; Pendrill, Ann-Marie; Reistad, Nina (2016-10-13). "Beyond velocity and acceleration: jerk, snap and higher derivatives". European Journal of Physics. 37 (6): 065008. Bibcode:2016EJPh...37f5008E. doi:10.1088/0143-0807/37/6/065008. hdl:10453/56556. ISSN 0143-0807. S2CID 19486813.
  2. ^ Cite error: The named reference PhysicsFAQ was invoked but never defined (see the help page).
  3. ^ "MATLAB Documentation: minsnappolytraj".
  4. ^ a b Cite error: The named reference Visser2004 was invoked but never defined (see the help page).
  5. ^ Cite error: The named reference Thompson was invoked but never defined (see the help page).