Derivatives of Position
For a position vector r that is a function of time t, the time derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, engineering and other sciences.
- Velocity
where dr is an infinitesimally small displacement (vector).
- Acceleration
- Jerk
These names for the first, second and third derivative of position are commonly used in basic kinematics. By extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the original displacement function. Such higher-order terms are required in order to accurately represent the displacement function as a sum of an infinite series, enabling several analytical techniques in engineering and physics.
Read more about this topic: Position (vector)
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