Fourth, fifth, and sixth derivatives of position

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thumb|Time-derivatives of position

In the physics field of kinematics, the fourth, fifth and sixth derivatives of position are generalizations of velocity and acceleration. They 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. These higher-order derivatives are less common than the first three;

The fourth derivative is referred to as snap, leading the fifth and sixth derivatives to be "sometimes somewhat facetiously" The fourth derivative is also called jounce. while minimum-jerk trajectories for robotic manipulators produce predictable motions that improve control performance and facilitate human-robot interaction.

(snap/jounce)

Snap,

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