Jerk 
Vector & Derivative Notation
The first derivative of position 
The second derivative of position 
Acceleration 
The third derivative of position 
Jerk is the first derivative of acceleration
Note that in the above notation we have shown implicitly that the kinematic variables are all measured with respect to time. In the main image for this page, the explicit notation is shown.
Jerk Equations
The “Jerk” is a fundamentally important quantity in physics. It is a vector quantity, which means it has both direction and magnitude. Further, it has been shown that a so-called Jerk Equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour.
Jerk Equations take the form of a third-order differential equation of the form:
When converted to an equivalent system of three ordinary first-order, non-linear, differential equations, Jerk Equations are the minimal setting for solutions showing chaotic behaviour.
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