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Summary of replies: First derivative of acceleration

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  • Summary of replies: First derivative of acceleration

    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 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
    Web page:

    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

    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 Feltham PhD
    Postdoctoral Researcher
    Movement Science Group
    School of Life Sciences
    Oxford Brookes University
    Headington Campus
    Gipsy Lane
    OX3 0BP
    United Kingdom

    T: +44 (0)1865 483272
    F: +44 (0)1865 483242


    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
    +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;

    Hi Jesse,
    I work in a biomechanics lab at marquette University. "Jerk" is the proper term for the first derivative of acceleration.

    Jon Wieser
    Research Technician
    Marquette University
    Department of Biomedical Engineering
    PO Box 1881
    Milwaukee, WI 53201-1881

    Fax 414-288-5987
    Jerk is the correct term but for impact type research "jolt" is also

    Jerk is the term taught in my PhD program.

    Rock Climbing
    Martial Arts

    60% of my life is spent recovering
    from what I do during the other 40%!

    Gannon White


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


    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.


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

    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

    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 C. Engbretson
    MsC Candidate
    Department of Mechanical and Materials Engineering
    Queen's University
    323 McLaughlin Hall

    Office: 613-533-3060

    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.

    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.


    Michael Orendurff
    Division Director
    Movement Science Laboratory
    Texas Scottish Rite Hospital for Children

    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 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.


    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.


    Best regards

    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.


    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.).


    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

    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

    hope it helps,

    Prof. Osmar Pinto Neto
    Department of Health & Kinesiology
    Texas A&M University - USA
    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.



    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 J. Bartsch, M.S.
    Cleveland Clinic Spine Research Laboratory
    Lutheran Hospital, 2-C
    1730 West 25th Street
    Cleveland, OH 44113

    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.


    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
    American College of Sports Medicine (ACSM)
    American Society of Biomechanics (ASB)
    International Society of Biomechanics (ISB)

    "Absence of evidence is not evidence of absence." ---Anonymous