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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
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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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