This article is about the physics concept of jerk. For other terms of jerk, see Jerk (disambiguation).

In physics, jerk (in British English, jolt), also called surge or lurch, is the rate of change of acceleration; more precisely, the derivative of acceleration with respect to time, the second derivative of velocity, or the third derivative of displacement.

Yank is the analog of force with respect to jerk: mass times jerk, or equivalently, the derivative of force with respect to time (this is only true non-relativistically; since mass is velocity dependent in relativistic physics, force is usually written as the first derivative of the momentum, while yank would be the second derivative. For force, it can be shown that dp/dt reduces to the familiar ma when v<

The units of jerk are metres per second cubed (m/s³). There is no universal agreement on the symbol for jerk, but j is commonly used.

Jerk is used at times in engineering, especially when building roller coasters. Some precision or fragile objects—such as passengers, who need time to sense stress changes and adjust their muscle tension, or suffer, e.g., whiplash—can be safely subjected not only to a maximum acceleration, but also to a maximum jerk. Jerk may be considered when the excitation of vibrations is a concern. A device which measures jerk is called a "jerkmeter."

Jerk is also important to consider in manufacturing processes. Rapid changes in acceleration of a cutting tool, for example going from zero to 100 percent instantaneously, result in theoretically infinite jerk. This can lead to premature tool wear and result in uneven lines of a cut. This is why modern motion controllers include such features as jerk limitation.

Higher derivatives of displacement are rarely necessary, and hence lack agreed names. The fourth derivative of position was considered in development of the Hubble Space Telescope's pointing control system, and called jounce. Many other suggestions have been made, such as jilt, jouse, jolt, and delta jerk. As more distinct terms that start with letters other than "j", snap, crackle, and pop have been proposed for the 4th, 5th, and 6th derivatives of displacement, respectively, with some nonzero positive value for tongue-in-cheek.

Jerk systems

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A jerk system is a system whose behavior is described by a jerk equation, which is an equation of the form (Sprott, 2003):

$\backslash frac\{d^3\; x\}\{d\; t^3\}=$

f\left(\frac{d^2 x}{d t^2},\frac{d x}{d t},x\right)

For example, certain simple electronic circuits may be designed which are described by a jerk equation. These are known as jerk circuits.

One of the most interesting properties of jerk systems is the possibility of chaotic behavior. In fact, certain well-known chaotic systems such as the Lorenz attractor and the Rössler map are conventionally described as a system of three first-order differential equations, but which may be combined into a single (although rather complicated) jerk equation.

An example of a jerk equation is:

$\backslash frac\{d^3\; x\}\{d\; t^3\}+A\backslash frac\{d^2\; x\}\{d\; t^2\}+\backslash frac\{d\; x\}\{d\; t\}-|x|+1=0.$

Where A is an adjustable parameter. This equation has a chaotic solution for A=3/5 and can be implemented with the following jerk circuit:

In the above circuit, all resistors are of equal value, except $R\_A=R/A=5R/3$, and all capacitors are of equal size. The dominant frequency will be $1/2\backslash pi\; R\; C$. The output of op amp 0 will correspond to the x variable, the output of 1 will correspond to the first derivative of x and the output of 2 will correspond to the second derivative.

References

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External links

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• What is the term used for the third derivative of position?, description of jerk in the Usenet Physics FAQ.

Classical mechanics | Physical quantity

Ruck | Jerk (physique) | 躍度 | Zryw | Jerk