Are there any practical applications of third order (or higher) derivatives and integrals?

looney_tunes

In terms of moving objects, the third order derivative of position as a function of time is called 'jerk', a measure of how quickly acceleration is changing with time. When I was in college, I learned to call it the surge. From Wikipedia: "If x(t) represents the position of an object at time t, then the higher-order derivatives of x have physical interpretations. The second derivative of x is the derivative of x?(t), the velocity, and by definition this is the object's acceleration. The third derivative of x is defined to be the jerk, and the fourth derivative is defined to be the jounce." http://en.wikipedia.org/wiki/Derivative http://en.wikipedia.org/wiki/Jerk_%28physics%29 Obviously, if you know about this function, you would be interested in the third antiderivative in order to find the position as a function of time. The fourth derivative, which corresponds to the rate of change of jerk with respect to time, is called the jounce. "The fourth, fifth and sixth derivatives of position as a function of time are 'sometimes somewhat facetiously' referred to as 'Snap', 'Crackle' and 'Pop'." http://en.wikipedia.org/wiki/Jounce Aug 20 12, 4:15 AM

timence

Absoultely! There are many...for example, in engineering and construction, finding particular areas underneath a specific shapes needs higher order calculus. There are also applications in economics, stronomy and physics (to name a few). http://calculus.nipissingu.ca/calc_app.html http://www.ehow.com/info_8524020_uses-calculus-real-life.html Aug 20 12, 4:18 AM

TimBentley

A specific use of jerk (the third-order derivative) is in roller coasters, where passengers and equipment can only safely withstand a maximum jerk. http://en.wikipedia.org/wiki/Jerk_%28physics%29#Applications http://thetartan.org/2007/4/16/scitech/work Aug 20 12, 8:21 AM

nautilator

Thanks, I had never heard of the jerk, jounce, and so forth before. The only application I knew of for higher orders like these was using a triple integral to find the volume of an object all three of whose sides vary. If a triple integral can be used in that way, is there any use for a quadruple integral (or higher) to extend that process for any additional practical applications? Aug 20 12, 8:34 PM