Editing Jerk (physics) (section)

== In elastically deformable matter ==

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| caption1 = Plane wave

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| caption2 = Cylindrical symmetry

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An [[Elastic Deformation|elastically deformable]] mass deforms under an applied force (or acceleration); the [[Deformation (engineering)|deformation]] is a function of its [[stiffness]] and the magnitude of the force. If the change in force is slow, the jerk is small, and the [[Wave propagation|propagation]] of deformation is considered instantaneous as compared to the change in acceleration. The distorted body acts as if it were in a [[Quasistatic loading|quasistatic regime]], and only a changing force (nonzero jerk) can cause propagation of mechanical waves (or [[electromagnetic wave]]s for a charged particle); therefore, for nonzero to high jerk, a [[shock wave]] 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]] through an elastically deformable material. Also shown, for angular jerk, are the deformation waves propagating in a circular pattern, which causes [[shear stress]] and possibly other [[Normal mode|modes]] of [[vibration]]. The reflection of waves along the boundaries cause constructive [[Wave interference|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.

[[File:Acceleration et deformation elastique.svg|thumbnail|left|Pole with massive top]]

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 ([[Damping ratio|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 [[Resonance|resonant mode]] because the larger wave components of the shock wave have higher frequencies and [[Fourier series|Fourier coefficients]].
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[[File:Chronogrammes loi sinusoidale par partie en vitesse.svg|thumbnail|right|Sinusoidal acceleration profile]]

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]], 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.{{clear}}