jerk (physics) - wikipedia, the free encyclopedia

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Jerk (physics)From Wikipedia, the free encyclopedia

In physics,jerk, also known asjolt(especially in British English), surgeand lurch, is the rate

of change of acceleration; that is, the derivative of acceleration with respect to time, the second

derivative of velocity, or the third derivative of position. Jerk is defined by any of the following

equivalent expressions:

where

is acceleration,

is velocity,

is position,is time.

Jerk is a vector, and there is no generally used term to describe its scalar magnitude (e.g.,

"speed" as the scalar magnitude for velocity).

The SI units of jerk are metres per second cubed (metres per second per second per second,

m/s3or ms3). There is no universal agreement on the symbol for jerk, butjis commonly used.

, Newton's notation for the derivative of acceleration, can also be used, especially when

"surge" or "lurch" is used instead of "jerk" or "jolt".

If acceleration can be felt by a body as the force (hence pressure) exerted by the object bringing

about the acceleration on the body, jerk can be felt as the change in this pressure. For example

a passenger in an accelerating vehicle with zero jerk will feel a constant force from the seat on

his or her body; whereas positive jerk will be felt as increasing force on the body, and negative

erk as decreasing force on the body.

Note also the existence of yankthe derivative of force with respect to time.

Applications

Normally concerning forces, speed and acceleration are used for analysis. For example, the

"jerk" produced by falling from outer space to the Earth is not particularly useful given the

gravitational acceleration changes very slowly. Sometimes the analysis has to extend to jerk for

a particular reason.

Jerk is often used in engineering, especially when building roller coasters.[1]Some precision or

fragile objects such as passengers, who need time to sense stress changes and adjust their

muscle tension or suffer conditions such as whiplash can be safely subjected not only to a

maximum acceleration, but also to a maximum jerk.[2]Even where occupant safety isn't an

issue, excessive jerk may result in an uncomfortable ride on elevators, trams and the like, and

(physics) - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Jerk_(physics)

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engineers expend considerable design effort to minimize it. Jerk may be considered when the

excitation of vibrations is a concern. A device that measures jerk is called a "jerkmeter".

Jerk is also important to consider in manufacturing processes. Rapid changes in acceleration of

a cutting tool can lead to premature tool wear and result in uneven cuts. This is why modern

motion controllers include jerk limitation features.

In mechanical engineering, jerk is considered, in addition to velocity and acceleration, in thedevelopment of cam profiles because of tribological implications and the ability of the actuated

body to follow the cam profile without chatter.[3]

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 seven segments defined by the following:[4]

acceleration build-up, with maximum positive jerk1.

constant maximum acceleration (zero jerk)2.

acceleration ramp-down, approaching the desired maximum velocity, with maximum

negative jerk

3.

constant maximum speed (zero jerk, zero acceleration)4.

deceleration build-up, approaching the desired deceleration, with maximum negative jerk5.

constant maximum deceleration (zero jerk)6.

deceleration ramp-down, approaching the desired position at zero velocity, with maximum

positive jerk

7.

If the initial and final positions are sufficiently close together, the maximum acceleration or

maximum velocity may never be reached.

Jerk systems


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Ajerk systemis a system whose behavior is described by ajerk equation, which is an equation

of the form (Sprott 2003):

For example, certain simple electronic circuits may be designed which are described by a jerk

equation. These are known asjerk 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 Rssler 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:

WhereAis 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.

Non-calculus explanation

Jerk can be difficult to conceptualize when it is defined in terms of calculus. When a force

(push or pull) is applied to an object, that object starts to move. As long as the force is applied,

the object will continue to speed up. When described in these terms, we are oversimplifying

slightly. We think along the lines that there is no force on the object, then all of the sudden

there is a force on the object. We do not think about how long it takes to apply the force.

However, in truth, the application of force does not instantly happen. A change always happens

over time. Jerk is the change in acceleration over time. Typically, the time of contact where a

force is applied is a split second.


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If you push on a wall, it takes a fraction of a second before you apply the full push. Your

fingertips will squoosh slightly as you begin to push. How long the squooshing takes determines

the jerk. If you push on a wall very slowly, you can actually feel your push increasing. In such a

case, the jerk is very low, because the change in force is happening over a relativel long time of

several seconds. Jerk happens when a force is applied and removed. But the whole time a force

is acting consistently on an object, there is no jerk. (This is because the acceleration is constant

when there is a constant force.)

How quickly the force starts its push or pull determines the yank and subsequently the jerk. In

most applications, it is not important how quickly the force is applied, and thus we typically

think of forces being applied instantaneously. In this way, jerk can seem counter-intuitive,

because it is not something people experience qualitatively on a daily basis.

If you take a piece of paper in your hands, holding it on both ends, you can pull very hard and

not tear the paper. But if you put your hands close together and then jerk on the paper, you can

tear it. You do not even have to pull hard. That's because you are using a high jerk (high

acceleration in short time) to tear the paper. The paper's fibers require a small amount of time to

respond to your pull and pull back. (In rheology, this is called the relaxation time.) If you pull

too fast, the paper simply snaps in half. You can similarly jerk on silly putty and snap it in half.

The speed at which you pull, and not how hard, determines whether the silly putty snaps or

stretches. To be clear, the key is how long it takes to go from zero acceleration to the full

application of acceleration. This is not the same thing as how long you pull on the paper, but

rather how long the snapping of the paper side to side lasts.

Equations

(yank: force per unit time)

(jerk: acceleration per unit time)

, following from Newton's second law divided by and the above two relations:


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The higher the force or acceleration, the higher the jerk. The shorter the time of change in

acceleration, such as a rollercoaster 'whipping' around a corner, the higher the jerk.

See also

Shock (mechanics)

JounceTerminal velocity

Notes

^http://thetartan.org/2007/4/16/scitech/work1.

^http://thetartan.org/2007/4/16/scitech/work2.

^Blair, G., "Making the Cam",Race Engine Technology10, September/October 20053.

^There is an idealization here that the jerk can be changed from zero to a constant non-zero value

instantaneously. However, since in classical mechanics all forces are caused by smooth fields, allderivatives of the position are continuous. On the other hand, this is also an idealization; in quantum

field theory particles do change momentum discontinuously.

4.

References

Sprott JC (2003). Chaos and Time-Series Analysis. Oxford University Press.

ISBN 0-19-850839-5.

Sprott JC (1997). "Some simple chaotic jerk functions" (http://sprott.physics.wisc.edu

/pubs/paper229.pdf) (PDF).Am J Phys65(6): 53743. Bibcode 1997AmJPh..65..537S(http://adsabs.harvard.edu/abs/1997AmJPh..65..537S) . doi:10.1119/1.18585

(http://dx.doi.org/10.1119%2F1.18585) . http://sprott.physics.wisc.edu

/pubs/paper229.pdf. Retrieved 2009-09-28.

Blair G (2005). "Making the Cam" (http://www.profblairandassociates.com

/pdfs/Camshaft%20RET%20010.pdf) (PDF).Race Engine Technology(010).

http://www.profblairandassociates.com/pdfs/Camshaft%20RET%20010.pdf. Retrieved

2009-09-29.

External links

What is the term used for the third derivative of position? (http://math.ucr.edu/home/baez

/physics/General/jerk.html) , description of jerk in the Usenet Physics FAQ

(http://math.ucr.edu/home/baez/physics/index.html) .

Mathematics of Motion Control Profiles (http://www.pmdcorp.com/news/articles

/html/Mathematics_of_Motion_Control_Profiles.cfm)

Retrieved from "http://en.wikipedia.org/w/index.php?title=Jerk_(physics)&oldid=487851918"

Categories: Classical mechanics Physical quantities

This page was last modified on 17 April 2012 at 16:06.


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