Jerk: Rate of Change of Acceleration

Kevin Kirby · Dec 13, 2009

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Just learned something new today from a discussion on Biomech-l.

The proper term for the time derivative of acceleration is "jerk".

The order of derivation of position is as follows:

1st derivative: velocity

2nd derivative: acceleration

3rd derivative: jerk

4th derivative: snap

5th derivative: crackle

6th derivative: pop

Here is the discussion:

Thanks to everyone who responded. Everyone agreed that jerk is the appropriate term, and several offered up the terms "snap", "crackle", and "pop" for higher derivatives of acceleration. Flash and Hogan's (1985) paper was also referred to my multiple people as an example of the use of jerk in biomechanical modeling:

Flash T, Hogan N: The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 1985, 5:103-168.

All responses are pasted below.

take care,
Jesse
_________________________________________
Jesse W. Young, Ph.D.
Assistant Professor
Department of Anatomy and Neurobiology
Northeastern Ohio Universities College
of Medicine (NEOUCOM)

Office phone: (330) 325-6304
Lab phone: (330) 325-6307
Fax: (330) 325-5916
Email: jwyoung@neoucom.edu
Web page: www.jessewyoung.com

_________________________________________
Dear Jesse,

My research focusses on the effect of visual information on bimanual
coordination in children with spastic hemiparetic cerebral palsy. These
children have a strong assymetry between body sides (i.e., they have a
more and a less impaired side), which is relatate to damage in the motor
cortex. My research article in which I calculated Jerk has been accepted
for publication in Motor Control and will hopefully be published in the
Spring issue.

It was deemed important to determine if changes in bimanual coordination
as a result of manipulating visual feedback reside in the more impaired
arm alone or in both the more and less impaired arm. A reduction in
symmetric coordination caused by improperly timed initiation and
disproportionate activation of independent muscle system, for example as a
result of spasticity, is likely to result in multiple acceleration peaks.
This can be measured as an increase in jerk compared to when coordination
is regular and smooth (Teulings et al., 1997; Flash & Hogan, 1985). Mean
jerk over the 2 cycles (unit: position/time3) was calculated in both
medial/lateral direction (x – axis) and posterior/anterior (y – axis)
direction by taking the third derivative of the x – and y – position.
Before jerk was calculated, position time signals of each trial were
filtered with a bi-directional 2nd order Butterworth filter. The cut-off
frequency was determined by taking 1 Hz lower than the frequency
ascertained with the residual analysis. A lower cut-off frequency was
taken to obtain a ‘smoother’ higher derivative of position data (Giakas &
Baltzopoulos, 1997). The range of the cut-off frequency was 2 – 10 Hz.
The level of jerk depends on the size and the duration of the movements
(Teulings et al., 1997), which in the present study could have differed
between participants because of their different anatomical proportions and
preferred movement time. Therefore, to compare intralimb stability between
participants, jerk was normalized for different size and duration of
movements in each trial (i.e., 2 cycles). This was done by multiplying
the integrated square jerk by time5/position2 and subsequently the square
root was taken so that normalized jerk was proportional with absolute
jerk.

So you need to consider the following very carefully:
- cut-off frequency when you filter your position signals (or velocity or
acceleration signals whatever you have).
- normalizing the jerk to time and position. In the attachment you will
find the formular I used. (n.b. normalized jerk is a unit less measure).

I hope if helps.

Best wishes,

Max

-- Max Feltham PhD Postdoctoral Researcher Movement Science Group School of Life Sciences Oxford Brookes University Headington Campus Gipsy Lane Oxford OX3 0BP United Kingdom T: +44 (0)1865 483272 F: +44 (0)1865 483242 E: mfeltham@brookes.ac.uk ------------------------------------------

Jesse, In a previous life I used to be involved in railway rolling stock design. There was an official specification book (part of the contract) defining all manner of requirements of the train provided for the tender. Under the performance requirements section there, things like maximum speed, and acceleration were listed. There was also a requirement for the rate of change of acceleration, and this was termed "jerk". I have not come across it in biomechanics literature, but this sort of thing is off topic for my current project so have not been looking in relevant areas. I would be confident that this is an accepted term unless better informed biomechanists say otherwise. Andrew Sims PhD Student University of New South Wales Sydney, Australia a.sims@student.unsw.edu.au +61 2 9385 3916 ------------------------------------------

Jerk is the appropriate term. If you want the next higher orders, it is snap, crackle and pop All the best; Fran ------------------------------------------

Hi Jesse, I work in a biomechanics lab at marquette University. "Jerk" is the proper term for the first derivative of acceleration. Jon Jon Wieser Research Technician Marquette University Department of Biomedical Engineering PO Box 1881 Milwaukee, WI 53201-1881 414-288-6184 Fax 414-288-5987 ------------------------------------------

Jerk is the correct term but for impact type research "jolt" is also used. ------------------------------------------

Jerk is the term taught in my PhD program. Running Kayaking Rock Climbing Martial Arts Hiking 60% of my life is spent recovering from what I do during the other 40%! Gannon White ------------------------------------------

Jesse, Jerk is a term I have always used in lectures, I find it gets a good laugh and wakes some of the students up!!! Regards Andy Greenhalgh ------------------------------------------

Have fun with your paper, because the term IS "jerk"! It's in all the textbooks, too. I think that engineers/mathmeticians/scientists got bored and this was a way to make math more interesting. Monica ------------------------------------------

You can also use "jolt". All the best, Ruth ------------------------------------------

Dear Jesse, In traditional structural mechanics and dynamics, the term is definitely 'jerk', and some people say that this is what the body really feels (awkward from) in e.g. an elevator. Biomechanics often has its own terms/definitions of common mechanical concepts, but in this case I do not know any such term. In your other question, torque is in itself not a common term in mechanics, at least not for the concept where it is used in biomechanics; it should be moment (torque might be the torsional moment in e.g. an engine axle). I do not know any special terms for the derivatives of this quantity, so 'rate of moment' should be correct. Anders Eriksson KTH Mechanics Stockholm, Sweden. ------------------------------------------

Jerk is the correct term, and the derivative of jerk is Snap if you are interested. Best Ronit Fuchs ------------------------------------------

As far as I know, "jerk" is the correct term for the time derivative of acceleration. However, I do not know of such a term for torque, but it would be in units of N*m/s, which is analogous to a Watt, if that is worth anything... Andrew ________________________________________ Andrew C. Engbretson MsC Candidate Department of Mechanical and Materials Engineering Queen's University 323 McLaughlin Hall Office: 613-533-3060 Email: engbretson@me.queensu.ca ------------------------------------------

I've heard it before as "discomfort," or "level of discomfort," although that was really for a specific application. I like that term. ------------------------------------------

Hi Jesse, Jerk is correct. It is the third derivative of displacement. John ------------------------------------------

Jesse, I professors in undergrad also used "jerk" to refer to the derivative of acceleration. ------------------------------------------

Yes, I think "jerk" is the preferred term. See if you can squeeze the second derivative "snap", third derivative "crackle" and fourth derivative "pop" into the paper. Cheers, Michael Orendurff Division Director Movement Science Laboratory Texas Scottish Rite Hospital for Children Dallas ------------------------------------------

Hi Dr. Young, I have seen jerk as the time derivative of acceleration in papers and text books. I think you can go ahead and use it, specially if it appeals to you. :) Do not know about the rate change for moments, though. Francisco ________________________________________________ Francisco J. Lopez-Valdes Center for Applied Biomechanics- University of Virginia European Center for Injury Prevention - Universidad de Navarra ------------------------------------------

Jerk is in fact the term you are looking for. ------------------------------------------

Hi Jesse, 'Jerk' has certainly been used in the biomechanics and motor control literature, although I can't find the references at the moment. Another interesting set of terms (although I'm not sure if someone was just making this up) are for the third, fourth and fifth derivatives of velocity: snap, crackle and pop. cheers, Bob ------------------------------------------

Hi Jesse, I recently used "jerk" to describe the rate of change in acceleration (see attachment). Adam Goodworth Biomedical Engineering Oregon Health & Science University ------------------------------------------

Hi Jesse, Yeah - it's jerk or jolt which appears to be less catchy to me. Cheers Best regards Gunther Dr. Gunther Paul Senior Research Fellow University of South Australia The Mawson Institute +61 8 830 23632 "Although mistakes reinforce learning, they don't help solve a problem." ------------------------------------------

Hi Jesse, Jerk, Jolt, Lurch or Surge take your pick (see link below). Though putting the word "jerk" in your paper would be very interesting. http://www.intospeed.com/Jerk_(physics)/encyclopedia.htm --Shaily ------------------------------------------

Velocity, acceleration, and jerk are the accepted terms of the first three derivatives of position. It is the fourth, fifth, and sixth derivatives that have never been officially named (though "snap," "crackle," and "pop" have been suggested.). Cheers, Tiffany Tiffany Zachry Research Engineer McKay Orthopaedic Research Laboratory Department of Orthopaedic Surgery University of Pennsylvania 412A Stemmler Hall 36th Street and Hamilton Walk Philadelphia, PA 19104-6081 Office: 215-573-3660 Email: zachry@mail.med.upenn.edu ------------------------------------------

Hi Jesse, funny question... "jerk" is a very common term in the motor behavior and motor neuroscience literature. This is an interesting paper that introduces the idea: The Journal of Neuroscience Vol. 4, No. 11, pp. 2745-2754 November 1984 "AN ORGANIZING PRINCIPLE FOR A CLASS OF VOLUNTARY MOVEMENTS’" by NEVILLE HOGAN hope it helps, Osmar. --- Prof. Osmar Pinto Neto Department of Health & Kinesiology Texas A&M University - USA and University of Camilo Castelo Branco - Brazil ------------------------------------------

There have been seminal papers that studied jerk. One of the hypothesis on the organization and control of motion put forward that in fact jerk was minimized: Flash and Hogan, 1985. So I would not look at this term suspiciously Alberto Borghese ------------------------------------------

Hi Jesse, Yes, I think 'jerk' is the appropriate term. While it doesn't appear often in the literature in general, I've seen it surface in some application quite frequently. For example, the hypothesis of the following paper is often referred to as the "minimum jerk model" of human motor control: Flash T, Hogan N: The coordination of arm movements: an experimentally confirmed mathematical model. J Neurosci 1985, 5:103-168. Rate of torque change, that's a tough one. I don't suppose 'instantaneous power' (i.e. torque*velocity) is appropriate? If not, then I think 'torque change rate' is the best choice, maybe abbreviated as dT/dt or something similar. Cheers, Todd ------------------------------------------

Jerk is the correct term and has been used for several decades in reference to human movement. I believe that Neville Hogan and Tamar Flash at MIT were the first to publish journal articles using the term in reference to human movement around 1985. Mechanical engineers use the terms jerk, snap, crackle and pop to refer to the third, fourth, fifth and sixth derivatives of position, respectively. ------------------------------------------

Hi Jesse- 'Jerk' to my knowledge is the most commonly used term to describe the acceleration rate. We've used jerk to supplement analysis of linear or angular acceleration for human impact studies. For torque, 'loading rate' has been sufficient for our applications, with the denotion that the units are N-m/s or lbf-ft/s indicating to the reader that the 'load' in this case is actually a moment. Warm regards, Adam ================================================== Adam J. Bartsch, M.S. Cleveland Clinic Spine Research Laboratory Lutheran Hospital, 2-C 1730 West 25th Street Cleveland, OH 44113 216.363.5749 ================================================== ------------------------------------------

Hi Jesse, I think jerk is the accepted term in physics for the first time derivative of acceleration. I have not often encountered jerk in musculoskeletal biomechanics papers, but I can't imagine anyone objecting to the use of this term. It is widely used in applied physics (for example in automobile research). The next three derivatives are snap, crackle, and pop, although these are a bit of a joke and most serious treatments just refer to them as the 2nd, 3rd, and 4th derivatives. I'm not familiar with a formal term to describe the time derivative of torque (or more generally of a moment). I think in biomechanics it is usually referred to as a loading rate, or more specifically the torque loading rate. Ross ------------------------------------------

Not to badmouth Wikipedia, but I don't really like it (Wikipedia, that is). The term "jerk" is, as far as I know, the accepted nomenclature for the third derivative of position (2nd derivative of velocity, 1st derivative of acceleration). This was explained to me by my Master's advisor, Dr. Mark Ricard, of the University of Texas-Arlington. He may know more details about the "derivation" of the term. Gary A. Christopher, Ph.D. Assistant Professor University of Great Falls 1301 20th Street South Great Falls, MT 59405 Office: 406-791-5383 Cell: 406-231-3631 gchristopher01@ugf.edu Memberships: American College of Sports Medicine (ACSM) American Society of Biomechanics (ASB) International Society of Biomechanics (ISB)
Click to expand...

adavies · Dec 14, 2009

And did you know

Momentum equals mass times velcoity!
Force equals mass times acceleration!
Yanks equals mass times jerk!
Tug equals mass times snap!
Snatch equals mass times crackle!
Shake equals mass times pop!

or so they say

Kiwi AD

adavies · Dec 15, 2009

Just a quick correction, thrid derivative should read

Yank equals mass times jerk

KiwiAD

fatboy · Dec 15, 2009

adavies said: ↑

Just a quick correction, thrid derivative should read

Yank equals mass times jerk

KiwiAD
Click to expand...

I prefer your original, because most of the yanks i've met have been jerks... :santa2:

David Smith · Dec 16, 2009

fatboy said: ↑

I prefer your original, because most of the yanks i've met have been jerks... :santa2:
Click to expand...

No! No! Bad taste old boy - Apology for some of our fellow American Arena colleagues wouldn't go amiss I believe. :bang:

Regards Dave Smith:craig:

fatboy · Dec 16, 2009

David Smith said: ↑

No! No! Bad taste old boy - Apology for some of our fellow American Arena colleagues wouldn't go amiss I believe. :bang:

Regards Dave Smith:craig:
Click to expand...

Aww i thought i was being nice, if i was being mean i would have said they were MASSive jerks...

:D

fatboy · Dec 16, 2009

adavies said: ↑

Tug equals mass times snap!
Snatch equals mass times crackle!
Shake equals mass times pop!

or so they say

Kiwi AD
Click to expand...

My breakfast could have been a whole lot more fun this morning.

Tomorrow i will be having a tug, snatch and shake...

just don't tell the HPC i did it at work!

Kevin Kirby · Dec 16, 2009

fatboy said: ↑

I prefer your original, because most of the yanks i've met have been jerks... :santa2:
Click to expand...

And how many of the 200+ million of those yanks have you met, Fat Boy??

fatboy · Dec 16, 2009

Kevin Kirby said: ↑

And how many of the 200+ million of those yanks have you met, Fat Boy??
Click to expand...

Just the important ones...

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