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

Look up jerk, jolt, surge, lurch in Wiktionary, the free dictionary.

In physics, jerk, jolt (esp in British English), 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. Jerk is described by the following equation: Look up jerk in Wiktionary, the free dictionary. ... Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... British English (BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the United Kingdom from forms used elsewhere in the Anglophone world. ... Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... For a non-technical overview of the subject, see Calculus. ... This article is about velocity in physics. ... In Newtonian mechanics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. ...

where

is acceleration,

– velocity,

– displacement

t stands for time.

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 << c). Jerk is a vector, and there is no generally used term to describe its scalar value. Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... This article is about velocity in physics. ... In Newtonian mechanics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. ... Look up time in Wiktionary, the free dictionary. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... For other uses, see Mass (disambiguation). ... In physics, a net force acting on a body causes that body to accelerate; that is, to change its velocity. ... The term mass in special relativity can be used in different ways, occasionally leading to confusion. ...

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. The SI system of units defines seven SI base units: physical units defined by an operational definition. ... This article is about the unit of length. ... This article is about the unit of time. ...

Jerk is often used 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." Engineering is the discipline of acquiring and applying knowledge of design, analysis, and/or construction of works for practical purposes. ... A typical roller coaster The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks. ... Whiplash is the common name for a hyper extension/flexion injury to the cervical, thoracic or lumbar spines. ...

Jerk is also important to consider in manufacturing processes. Rapid changes in acceleration of a cutting tool, such as going from 0 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. Manufacturing (from Latin manu factura, making by hand) is the use of tools and labor to make things for use or sale. ... Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ...

Higher derivatives of displacement are rarely necessary, and hence lack agreed-on 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", the term snap has been proposed for the 4th derivative of position, with "crackle" and "pop" having been suggested - facetiously - as names for the 5th and 6th derivatives.^[1] The Hubble Space Telescope (HST) is a telescope in orbit around the Earth, named after astronomer Edwin Hubble. ... The word Jounce or jounce has several possible meanings: a band, from New York with Danny Tamberelli a jerk, the fourth derivative of position (symbol x) This is a disambiguation page: a list of articles associated with the same title. ... Look up jounce in Wiktionary, the free dictionary. ... Snap, Crackle and Pop as they are portrayed in Australia and New Zealand today Snap, Crackle and Pop! are the cartoon mascots of Kelloggs breakfast cereal Rice Krispies (Rice Bubbles in Australia). ...

Third order motion profile

In motion control, a common need is to move a system from one steady position to another (point-to-point motion). Following the fastest possible motion within an allowed maximum value for speed, acceleration, and jerk, will result in a third-order motion profile as illustrated below:

Image File history File links 3rd_order_motion_profile. ...

The motion profile consists of up to 7 segments defined by the following equations:

1. acceleration build-up, with constant jerk = maxJerk
2. move with constant acceleration, with jerk = 0
3. approaching the desired maximum velocity, with jerk = -maxJerk
4. approaching the desired deceleration, with jerk = -maxJerk
5. move with constant deceleration, with jerk = 0
6. approaching the desired position, with jerk = maxJerk

For shorter motions, the maximum acceleration or maximum velocity may never be reached.

Jerk systems

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

1. move with constant velocity, with jerk = 0 and acceleration = 0

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. For other uses, see Chaos Theory (disambiguation). ... A plot of the trajectory Lorenz system for values ρ=28, σ = 10, β = 8/3 A trajectory of Lorenzs equations, rendered as a metal wire to show direction and three-dimensional structure The Lorenz attractor is a chaotic map, noted for its butterfly shape. ... In 1979 Otto Rössler found the inspiration from a Taffy-pulling machine for his Non-linear three-dimensional deterministic dynamical system. ...

An example of a jerk equation is:

.

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 / 2πRC. 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. Image File history File links Download high resolution version (922x571, 37 KB) Summary Example of a jerk circuit. ... A 741 operational amplifier in a TO-5 metal can package An operational amplifier, usually referred to as an op-amp for brevity, is a DC-coupled high-gain electronic voltage amplifier with Differential Inputs and, usually, a single output. ...

See also

• Radiation reaction

In the physics of electromagnetism, the radiation reaction is the recoil force felt by a charged object that is emitting electromagnetic radiation. ...

References

• Sprott, Julien Clinton (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0-19-850839-5 and ISBN 978-0-19-850839-7. 
• Am. J. Phys., Vol. 65, No. 6, Pg. 538, June 1997

External links

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