Cookies help us deliver our services. By using our services, you agree to our use of cookies.

# 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:

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

The following equations are used for constant jounce:

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

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

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

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

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 ==