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In
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, jerk or jolt is the rate at which an object's
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
changes with respect to time. It is a
vector quantity In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors ac ...
(having both magnitude and direction). Jerk is most commonly denoted by the symbol and expressed in m/s3 (
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
s) or standard gravities per second (''g''0/s).


Expressions

As a vector, jerk can be expressed as the first
time derivative A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as t. Notation A variety of notations are used to denote th ...
of
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
, second time derivative of
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity i ...
, and third time derivative of position: \mathbf j(t) = \frac = \frac = \frac where * is acceleration * is velocity * is position * is time Third-order
differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
of the form J\left(\overset, \ddot, \dot, x\right) = 0 are sometimes called ''jerk equations''. When converted to an equivalent system of three ordinary
first-order In mathematics and other formal sciences, first-order or first order most often means either: * "linear" (a polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of hig ...
non-linear In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
differential equations, jerk equations are the minimal setting for solutions showing chaotic behaviour. This condition generates mathematical interest in ''jerk systems''. Systems involving fourth-order derivatives or higher are accordingly called ''hyperjerk systems''.


Physiological effects and human perception

Human body position is controlled by balancing the forces of
antagonistic muscles An antagonist is a character in a story who is presented as the chief foe of the protagonist. Etymology The English word antagonist comes from the Greek ἀνταγωνιστής – ''antagonistēs'', "opponent, competitor, villain, enemy, ri ...
. In balancing a given force, such as holding up a weight, the
postcentral gyrus In neuroanatomy, the postcentral gyrus is a prominent gyrus in the lateral parietal lobe of the human brain. It is the location of the primary somatosensory cortex, the main sensory receptive area for the sense of touch. Like other sensory areas, ...
establishes a
control loop A control loop is the fundamental building block of industrial control systems. It consists of all the physical components and control functions necessary to automatically adjust the value of a measured process variable (PV) to equal the value of ...
to achieve the desired equilibrium. If the force changes too quickly, the muscles cannot relax or tense fast enough and overshoot in either direction, causing a temporary loss of control. The reaction time for responding to changes in force depends on physiological limitations and the
attention Attention is the behavioral and cognitive process of selectively concentrating on a discrete aspect of information, whether considered subjective or objective, while ignoring other perceivable information. William James (1890) wrote that "Att ...
level of the brain: an ''expected'' change will be stabilized faster than a ''sudden'' decrease or increase of load. To avoid vehicle passengers losing control over body motion and getting injured, it is necessary to limit the exposure to both the maximum force (acceleration) ''and'' maximum jerk, since time is needed to adjust muscle tension and adapt to even limited stress changes. Sudden changes in acceleration can cause injuries such as whiplash. Excessive jerk may also result in an uncomfortable ride, even at levels that do not cause injury. Engineers expend considerable design effort minimizing "jerky motion" on
elevator An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They ...
s,
tram A tram (called a streetcar or trolley in North America) is a rail vehicle that travels on tramway tracks on public urban streets; some include segments on segregated right-of-way. The tramlines or networks operated as public transport ...
s, and other conveyances. For example, consider the effects of acceleration and jerk when riding in a car: * Skilled and experienced drivers can accelerate smoothly, but beginners often provide a ''jerky'' ride. When changing gears in a car with a foot-operated clutch, the accelerating force is limited by engine power, but an inexperienced driver can cause severe jerk because of intermittent force closure over the clutch. * The feeling of being pressed into the seats in a high-powered sports car is due to the acceleration. As the car launches from rest, there is a large positive jerk as its acceleration rapidly increases. After the launch, there is a small, sustained negative jerk as the force of air resistance increases with the car's velocity, gradually decreasing acceleration and reducing the force pressing the passenger into the seat. When the car reaches its top speed, the acceleration has reached 0 and remains constant, after which there is no jerk until the driver decelerates or changes direction. * When braking suddenly or during collisions, passengers whip forward with an initial acceleration that is larger than during the rest of the braking process because muscle tension regains control of the body quickly after the onset of braking or impact. These effects are not modeled in vehicle testing because
cadaver A cadaver or corpse is a dead human body that is used by medical students, physicians and other scientists to study anatomy, identify disease sites, determine causes of death, and provide tissue to repair a defect in a living human being. Stud ...
s and crash test dummies do not have active muscle control. * To minimize the effects of a jerk, curves along roads are designed to be clothoids as are railroad curves and roller coaster loops.


Force, acceleration, and jerk

For a constant mass , acceleration is directly proportional to force according to
Newton's second law of motion Newton's laws of motion are three basic Scientific law, laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at re ...
: \mathbf = m \mathbf In
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classi ...
of rigid bodies, there are no ''forces'' associated with the derivatives of acceleration; however, physical systems experience oscillations and deformations as a result of jerk. In designing the
Hubble Space Telescope The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most vers ...
,
NASA The National Aeronautics and Space Administration (NASA ) is an independent agency of the US federal government responsible for the civil space program, aeronautics research, and space research. NASA was established in 1958, succeedin ...
set limits on both jerk and
jounce In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. Unlike ...
. The
Abraham–Lorentz force In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation by self-interaction. It is also ca ...
is the
recoil Recoil (often called knockback, kickback or simply kick) is the rearward thrust generated when a gun is being discharged. In technical terms, the recoil is a result of conservation of momentum, as according to Newton's third law the force r ...
force on an accelerating charged particle emitting radiation. This force is proportional to the particle's jerk and to the square of its charge. The
Wheeler–Feynman absorber theory The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assu ...
is a more advanced theory, applicable in a relativistic and quantum environment, and accounting for
self-energy In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between ...
.


In an idealized setting

Discontinuities in acceleration do not occur in real-world environments because of deformation,
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
effects, and other causes. However, a jump-discontinuity in acceleration and, accordingly, unbounded jerk are feasible in an idealized setting, such as an idealized point mass moving along a
piecewise In mathematics, a piecewise-defined function (also called a piecewise function, a hybrid function, or definition by cases) is a function defined by multiple sub-functions, where each sub-function applies to a different interval in the domain. P ...
smooth, whole continuous path. The jump-discontinuity occurs at points where the path is not smooth. Extrapolating from these idealized settings, one can qualitatively describe, explain and predict the effects of jerk in real situations. Jump-discontinuity in acceleration can be modeled using a
Dirac delta function In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the enti ...
in jerk, scaled to the height of the jump. Integrating jerk over time across the Dirac delta yields the jump-discontinuity. For example, consider a path along an arc of radius , which tangentially connects to a straight line. The whole path is continuous, and its pieces are smooth. Now assume a point particle moves with constant speed along this path, so its
tangential acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
is zero. The centripetal acceleration given by is normal to the arc and inward. When the particle passes the connection of pieces, it experiences a jump-discontinuity in acceleration given by , and it undergoes a jerk that can be modeled by a Dirac delta, scaled to the jump-discontinuity. For a more tangible example of discontinuous acceleration, consider an ideal spring–mass system with the mass oscillating on an idealized surface with friction. The force on the mass is equal to the vector sum of the spring force and the kinetic frictional force. When the velocity changes sign (at the maximum and minimum displacements), the magnitude of the force on the mass changes by twice the magnitude of the frictional force, because the spring force is continuous and the frictional force reverses direction with velocity. The jump in acceleration equals the force on the mass divided by the mass. That is, each time the mass passes through a minimum or maximum displacement, the mass experiences a discontinuous acceleration, and the jerk contains a Dirac delta until the mass stops. The static friction force adapts to the residual spring force, establishing equilibrium with zero net force and zero velocity. Consider the example of a braking and decelerating car. The
brake pad Brake pads are a component of disc brakes used in automotive and other applications. Brake pads are composed of steel backing plates with friction material bound to the surface that faces the disc brake rotors. Function Brake pads convert the kin ...
s generate kinetic frictional forces and constant braking
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
s on the disks (or
drums A drum kit (also called a drum set, trap set, or simply drums) is a collection of drums, cymbals, and other auxiliary percussion instruments set up to be played by one person. The player (drummer) typically holds a pair of matching drumsticks ...
) of the wheels. Rotational velocity decreases linearly to zero with constant angular deceleration. The frictional force, torque, and car deceleration suddenly reach zero, which indicates a Dirac delta in physical jerk. The Dirac delta is smoothed down by the real environment, the cumulative effects of which are analogous to damping of the physiologically perceived jerk. This example neglects the effects of tire sliding, suspension dipping, real deflection of all ideally rigid mechanisms, etc. Another example of significant jerk, analogous to the first example, is the cutting of a rope with a particle on its end. Assume the particle is oscillating in a circular path with non-zero centripetal acceleration. When the rope is cut, the particle's path changes abruptly to a straight path, and the force in the inward direction changes suddenly to zero. Imagine a monomolecular fiber cut by a laser; the particle would experience very high rates of jerk because of the extremely short cutting time.


In rotation

Consider a rigid body rotating about a fixed axis in an
inertial reference frame In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
. If its angular position as a function of time is , the angular velocity, acceleration, and jerk can be expressed as follows: *
Angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
, \omega(t)=\dot\theta(t)=\frac , is the time derivative of . *
Angular acceleration In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular accelera ...
, \alpha(t)=\dot\omega(t)=\frac , is the time derivative of . * Angular jerk, \zeta(t) = \dot (t) =\ddot\omega(t) = \overset(t), is the time derivative of . Angular acceleration equals the
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
acting on the body, divided by the body's
moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular accele ...
with respect to the momentary axis of rotation. A change in torque results in angular jerk. The general case of a rotating rigid body can be modeled using kinematic screw theory, which includes one axial
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
, angular velocity , and one polar
vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
, linear velocity . From this, the angular acceleration is defined as \boldsymbol(t) = \frac \boldsymbol(t)= \dot (t) and the angular jerk is given by \boldsymbol\zeta(t) = \frac \boldsymbol(t)=\dot(t) = \ddot(t) For example, consider a Geneva drive, a device used for creating intermittent rotation of a driven wheel (the blue wheel in the animation) by continuous rotation of a driving wheel (the red wheel in the animation). During one cycle of the driving wheel, the driven wheel's angular position changes by 90 degrees and then remains constant. Because of the finite thickness of the driving wheel's fork (the slot for the driving pin), this device generates a discontinuity in the angular acceleration , and an unbounded angular jerk in the driven wheel. Jerk does not preclude the Geneva drive from being used in applications such as movie projectors and cams. In movie projectors, the film advances frame-by-frame, but the projector operation has low noise and is highly reliable because of the low film load (only a small section of film weighing a few grams is driven), the moderate speed (2.4 m/s), and the low friction. With cam drive systems, use of a dual cam can avoid the jerk of a single cam; however, the dual cam is bulkier and more expensive. The dual-cam system has two cams on one axle that shifts a second axle by a fraction of a revolution. The graphic shows step drives of one-sixth and one-third rotation per one revolution of the driving axle. There is no radial clearance because two arms of the stepped wheel are always in contact with the double cam. Generally, combined contacts may be used to avoid the jerk (and wear and noise) associated with a single follower (such as a single follower gliding along a slot and changing its contact point from one side of the slot to the other can be avoided by using two followers sliding along the same slot, one side each).


In elastically deformable matter

An elastically deformable mass deforms under an applied force (or acceleration); the deformation is a function of its
stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a ...
and the magnitude of the force. If the change in force is slow, the jerk is small, and the
propagation Propagation can refer to: *Chain propagation in a chemical reaction mechanism *Crack propagation, the growth of a crack during the fracture of materials * Propaganda, non-objective information used to further an agenda * Reproduction, and other for ...
of deformation is considered instantaneous as compared to the change in acceleration. The distorted body acts as if it were in a quasistatic regime, and only a changing force (nonzero jerk) can cause propagation of mechanical waves (or
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
s for a charged particle); therefore, for nonzero to high jerk, a
shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...
and its propagation through the body should be considered. The propagation of deformation is shown in the graphic "Compression wave patterns" as a compressional
plane wave In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, ...
through an elastically deformable material. Also shown, for angular jerk, are the deformation waves propagating in a circular pattern, which causes
shear stress Shear stress, often denoted by ( Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. '' Normal stress'', on ...
and possibly other
modes Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
of
vibration Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic, such as the motion of a pendulum—or random, su ...
. The reflection of waves along the boundaries cause constructive interference patterns (not pictured), producing stresses that may exceed the material's limits. The deformation waves may cause vibrations, which can lead to noise, wear, and failure, especially in cases of resonance. The graphic captioned "Pole with massive top" shows a block connected to an elastic pole and a massive top. The pole bends when the block accelerates, and when the acceleration stops, the top will oscillate ( damped) under the regime of pole stiffness. One could argue that a greater (periodic) jerk might excite a larger amplitude of oscillation because small oscillations are damped before reinforcement by a shock wave. One can also argue that a larger jerk might increase the probability of exciting a resonant mode because the larger wave components of the shock wave have higher frequencies and Fourier coefficients. To reduce the amplitude of excited stress waves and vibrations, one can limit jerk by shaping motion and making the acceleration continuous with slopes as flat as possible. Due to limitations of abstract models, algorithms for reducing vibrations include higher derivatives, such as
jounce In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. Unlike ...
, or suggest continuous regimes for both acceleration and jerk. One concept for limiting jerk is to shape acceleration and deceleration sinusoidally with zero acceleration in between (see graphic captioned "Sinusoidal acceleration profile"), making the speed appear sinusoidal with constant maximum speed. The jerk, however, will remain discontinuous at the points where acceleration enters and leaves the zero phases.


In the geometric design of roads and tracks

Roads and tracks are designed to limit the jerk caused by changes in their curvature. On railways, designers use 0.35 m/s3 as a design goal and 0.5 m/s3 as a maximum.
Track transition curves A track transition curve, or spiral easement, is a mathematically-calculated curve on a section of highway, or railroad track, in which a straight section changes into a curve. It is designed to prevent sudden changes in lateral (or centripeta ...
limit the jerk when transitioning from a straight line to a curve, or vice versa. Recall that in constant-speed motion along an arc, jerk is zero in the tangential direction and nonzero in the inward normal direction. Transition curves gradually increase the curvature and, consequently, the centripetal acceleration. An
Euler spiral An Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of a circular curve is equal to the reciprocal of the radius). Euler spirals are also commonly referred to as spiros, clothoids, or Cornu spirals. E ...
, the theoretically optimum transition curve, linearly increases centripetal acceleration and results in constant jerk (see graphic). In real-world applications, the plane of the track is inclined (
cant Cant, CANT, canting, or canted may refer to: Language * Cant (language), a secret language * Beurla Reagaird, a language of the Scottish Highland Travellers * Scottish Cant, a language of the Scottish Lowland Travellers * Shelta or the Cant, a la ...
) along the curved sections. The incline causes vertical acceleration, which is a design consideration for wear on the track and embankment. The Wiener Kurve (Viennese Curve) is a patented curve designed to minimize this wear.
Rollercoaster A roller coaster, or rollercoaster, is a type of amusement ride that employs a form of elevated railroad track designed with tight turns, steep slopes, and sometimes inversions. Passengers ride along the track in open cars, and the rides are ...
s are also designed with track transitions to limit jerk. When entering a loop, acceleration values can reach around 4''g'' (40 m/s2), and riding in this high acceleration environment is only possible with track transitions. S-shaped curves, such as figure eights, also use track transitions for smooth rides.


In motion control

In
motion control Motion control is a sub-field of automation, encompassing the systems or sub-systems involved in moving parts of machines in a controlled manner. Motion control systems are extensively used in a variety of fields for automation purposes, includi ...
, the design focus is on straight, linear motion, with the need to move a system from one steady position to another (point-to-point motion). The design concern from a jerk perspective is vertical jerk; the jerk from tangential acceleration is effectively zero since linear motion is non-rotational. Motion control applications include passenger
elevator An elevator or lift is a cable-assisted, hydraulic cylinder-assisted, or roller-track assisted machine that vertically transports people or freight between floors, levels, or decks of a building, vessel, or other structure. They ...
s and machining tools. Limiting vertical jerk is considered essential for elevator riding convenience. ISO 18738 specifies measurement methods for elevator ride quality with respect to jerk, acceleration, vibration, and noise; however, the standard does specify levels for acceptable or unacceptable ride quality. It is reported that most passengers rate a vertical jerk of 2 m/s3 as acceptable and 6 m/s3 as intolerable. For hospitals, 0.7 m/s3 is the recommended limit. A primary design goal for motion control is to minimize the transition time without exceeding speed, acceleration, or jerk limits. Consider a third-order motion-control profile with quadratic ramping and deramping phases in velocity (see figure). This motion profile consists of the following seven segments: # Acceleration build up — positive jerk limit; linear increase in acceleration to the positive acceleration limit; quadratic increase in velocity # Upper acceleration limit — zero jerk; linear increase in velocity # Acceleration ramp down — negative jerk limit; linear decrease in acceleration; (negative) quadratic increase in velocity, approaching the desired velocity limit # Velocity limit — zero jerk; zero acceleration # Deceleration build up — negative jerk limit; linear decrease in acceleration to the negative acceleration limit; (negative) quadratic decrease in velocity # Lower deceleration limit — zero jerk; linear decrease in velocity # Deceleration ramp down — positive jerk limit; linear increase in acceleration to zero; quadratic decrease in velocity; approaching the desired position at zero speed and zero acceleration Segment four's time period (constant velocity) varies with distance between the two positions. If this distance is so small that omitting segment four would not suffice, then segments two and six (constant acceleration) could be equally reduced, and the constant velocity limit would not be reached. If this modification does not sufficiently reduce the crossed distance, then segments one, three, five, and seven could be shortened by an equal amount, and the constant acceleration limits would not be reached. Other motion profile strategies are used, such as minimizing the square of jerk for a given transition time and, as discussed above, sinusoidal-shaped acceleration profiles. Motion profiles are tailored for specific applications including machines, people movers, chain hoists, automobiles, and robotics.


In manufacturing

Jerk is an important consideration in
manufacturing Manufacturing is the creation or production of goods with the help of equipment, labor, machines, tools, and chemical or biological processing or formulation. It is the essence of secondary sector of the economy. The term may refer to ...
processes. Rapid changes in acceleration of a cutting tool can lead to premature tool wear and result in uneven cuts; consequently, modern
motion controllers In video games and entertainment systems, a motion controller is a type of game controller that uses accelerometers or other sensors to track motion and provide input. History Motion controllers using accelerometers are used as controllers for ...
include jerk limitation features. In mechanical engineering, jerk, in addition to velocity and acceleration, is considered in the development of cam profiles because of tribological implications and the ability of the actuated body to follow the cam profile without chatter. Jerk is often considered when vibration is a concern. A device that measures jerk is called a "jerkmeter".


Further derivatives

Further time derivatives have also been named, as snap or jounce (fourth derivative), crackle (fifth derivative), and pop (sixth derivative). However, time derivatives of position of higher order than four appear rarely. The terms ''snap'', ''crackle'', and ''pop''for the fourth, fifth, and sixth derivatives of positionwere inspired by the advertising mascots Snap, Crackle, and Pop.


See also

* Geomagnetic jerk *
Shock (mechanics) A mechanical or physical shock is a sudden acceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation. Shock describes matter subject to extreme rates of force with respect to tim ...
* Yank


References

* * *


External links


What is the term used for the third derivative of position?
description of jerk in th
Mathematics of Motion Control ProfilesElevator-Ride-QualityElevator manufacturer brochurePatent of ''Wiener Kurve''

Description of ''Wiener Kurve''
{{Classical mechanics derived SI units Acceleration Classical mechanics Kinematic properties Temporal rates Time in physics Vector physical quantities