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jounce

jounce

definition : jounce

In physics, jounce, also known as snap, is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. Equivalently, it is second derivative of acceleration or the third derivative of velocity. Jounce is defined by any of the following equivalent expressions:

:\vec s = \frac{d \,\vec \jmath}{dt} = \frac{d^2 \vec a}{dt^2} = \frac{d^3 \vec v}{dt^3} = \frac{d^4 \vec r}{dt^4}.

The following equations are used for constant jounce:

:\vec \jmath = \vec \jmath_0 + \vec s t,

:\vec a = \vec a_0 + \vec \jmath_0 t + \frac{1}{2} \vec s t^2,

:\vec v = \vec v_0 + \vec a_0 t + \frac{1}{2} \vec \jmath_0 t^2 + \frac{1}{6} \vec s t^3,

:\vec r = \vec r_0 + \vec v_0 t + \frac{1}{2} \vec a_0 t^2 + \frac{1}{6} \vec \jmath_0 t^3 + \frac{1}{24} \vec s t^4,

where

:\vec s is constant jounce, :\vec \jmath_0 is initial jerk, :\vec \jmath is final jerk, :\vec a_0 is initial acceleration, :\vec a is final acceleration, :\vec v_0 is initial velocity, :\vec v is final velocity, :\vec r_0 is initial position, :\vec r is final position, :t is time between initial and final states.

The notation \vec s (used by Visser referred to as snap, crackle, and pop respectively. However, time derivatives of position of higher order than four appear rarely.

== References ==

== External links ==

*[https://arxiv.org/pdf/gr-qc/0411131 Cosmography: cosmology without the Einstein equations], Matt Visser, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, 2004.

Category:Physical quantities Category:Time in physics Category:Acceleration

Texte soumis à la licence CC-BY-SA. Source : Article https://en.wikipedia.org/wiki/Jounce de Wikipédia

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