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Information about Jerk

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


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 position. Jerk is described by the following equation:
where
is acceleration,
– velocity,
– displacement
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.

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 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."

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, somewhat facetiously.[1]

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:



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# approaching the desired deceleration, with jerk = -maxJerk
  4. move with constant deceleration, with jerk = 0
  5. 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.

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 , and all capacitors are of equal size. The dominant frequency will be . 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.

Kinematics
← Integrate ... Differentiate →
Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Snap

See also

References

External links

Jerk may refer to one of the following:
  • Clean and jerk, the second stage of the Olympic weightlifting exercise
  • Hypnic jerk, an involuntary muscle twitch during the transition from wakefulness to sleep

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Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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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.
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acceleration is defined as the rate of change of velocity, or, equivalently, as the second derivative of position. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in metres/second² (m·s-²).
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derivative is a measurement of how a function changes when the values of its inputs change. Loosely speaking, a derivative can be thought of as how much a quantity is changing at some given point.
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velocity is defined as the rate of change of position. It is a vector physical quantity, both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second (m/s). The scalar absolute value (magnitude) of velocity is speed.
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acceleration is defined as the rate of change of velocity, or, equivalently, as the second derivative of position. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in metres/second² (m·s-²).
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velocity is defined as the rate of change of position. It is a vector physical quantity, both speed and direction are required to define it. In the SI (metric) system, it is measured in meters per second (m/s). The scalar absolute value (magnitude) of velocity is speed.
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In physics, displacement is the vector that specifies the position of a point or a particle in reference to an origin or to a previous position. The vector directs from the reference point to the current position.
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time.

One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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In physics, yank is the derivative of force with respect to time or mass multiplied by jerk. Though not universally accepted as an official term for this quantity, the term yank is commonly used among physics enthusiasts.
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
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In physics, force is an action or agency that causes a body of mass m to accelerate. It may be experienced as a lift, a push, or a pull. The acceleration of the body is proportional to the vector sum of all forces acting on it (known as net force or resultant force).
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relativistic mass is also used, this occasionally leads to confusion.

The invariant mass of an object (also known as the rest mass, intrinsic mass or proper mass) is an observer-independent quantity that is synonymous with mass.
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The international system (SI) of units defines seven SI base units: physical units defined by an operational definition.

All other physical units can be derived from these base units: these are known as SI derived units. Derivation is by dimensional analysis.
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1 metre =
SI units
1000 mm 0 cm
US customary / Imperial units
0 ft 0 in
The metre or meter[1](symbol: m) is the fundamental unit of length in the International System of Units (SI).
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second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time.

SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g.
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Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. The American Engineers' Council for Professional Development, also known as ECPD,[1] (later ABET [2]
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roller coaster (the term jet coaster is sometimes used for roller coasters in Japan) is a popular amusement ride developed for amusement parks and modern theme parks. LaMarcus Adna Thompson patented the first roller coaster on January 20 1885.
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MeSH D014911 Whiplash is the common name for neck sprains, such as those caused by hyper extension/flexion injury to the cervical, thoracic or lumbar spines. The injury is referred to as "whiplash" due to the neck or back being thrown forwards and/or backwards at a rapid
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Manufacturing (from Latin manu factura, "making by hand") is the use of tools and labor to make things for use or sale. The term may refer to a vast range of human activity, from handicraft to high tech, but is most commonly applied to industrial production, in which raw
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acceleration is defined as the rate of change of velocity, or, equivalently, as the second derivative of position. It is thus a vector quantity with dimension length/time². In SI units, acceleration is measured in metres/second² (m·s-²).
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The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end") which arise in philosophy, mathematics, and theology.
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Hubble Space Telescope (HST) is a telescope in orbit around the Earth, named after astronomer Edwin Hubble. Its position outside the Earth's atmosphere provides significant advantages over ground-based telescopes — images are not blurred by the atmosphere, there is no
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In physics, snap or jounce is the fourth derivative of the displacement vector with respect to time, with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively; in other words, the snap is the rate of change of the jerk with respect to
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Snap, Crackle and Pop! are the cartoon mascots of Kellogg's breakfast cereal Rice Krispies (Rice Bubbles in Australia).

History

The three elf characters were originally designed by illustrator Vernon Grant and made their debut in 1933.
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chaos theory describes the behavior of certain nonlinear dynamical systems that under specific conditions exhibit dynamics that are sensitive to initial conditions (popularly referred to as the butterfly effect).
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Lorenz attractor is a 3-dimensional structure corresponding to the long-term behavior of a chaotic flow, noted for its butterfly shape. The map shows how the state of a dynamical system (the three variables of a three-dimensional system) evolves over time in a complex,
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Rössler attractor (IPA pronunciation: [ɹøslə ətɹæk.tɘ]) is the attractor for the Rössler system, a system of three non-linear ordinary differential equations.
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