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Posted: Thu Apr 30, 2009 1:57 am UTC
First sorry for the math equations, i don't know TeX.

Okay, the basic equations of motion are driving me nuts. I know the basics of Sf=Si+Vi(t)+1/2a(t)^2 but that works for constant acceleration. where Sf is final position, Si is initial position, Vi is initial velocity, t is time, and a is acceleration.

Is what I am wondering is what is the basic equations for mechanics with a non zero jerk?

since jerk is da/dt it would have to be J (if J symbol for jerk, i know its already impulse) Jt^3 so the units would end up as meters. and from calculus im thinking it would be 1/6J(t)^3, so the acceleration would be 1/2a(t)^2.

But if I put this in all I can come up with would be Sf=Si+Vi(t)+1/2ai(t)^2+1/6J(t)^3, where ai is initial acceleration, so when I take the derivative ill end up eventually getting J=J. since 3rd derivative of s needs to be j, 2nd a, and 1st v. by definition.

So am I getting this correct, or am I missing something? What is the correct equation if anyone knows it. This is all I can come up with, without doing a differential equation or something, and I am not really sure how I would make it. I can not find this equation anywhere online, I cant google and find anything past basic physics 1 mechanics. thanks for any help

Posted: Thu Apr 30, 2009 3:44 am UTC
There are only 1 set of equations for constant acceleration. There is an infinite number of possible accelerations. The way to get the equations of motion is by integrating acceleration to get velocity, and then integrating velocity to get position.

Posted: Thu Apr 30, 2009 3:52 am UTC
Your equations seem right to me, I just did the integrating.

Posted: Thu Apr 30, 2009 1:31 pm UTC
O whoops I didn't see that you assumed a constant jerk.

As a side note, I just noticed if you keep doing this you get a Taylor series, and that method is a good way to derive the Taylor series. (This may be the only way to derive it but I always forget how it was taught in class).

Posted: Thu Apr 30, 2009 2:30 pm UTC
ecshafer wrote:First sorry for the math equations, i don't know TeX.

Okay, the basic equations of motion are driving me nuts. I know the basics of Sf=Si+Vi(t)+1/2a(t)^2 but that works for constant acceleration. where Sf is final position, Si is initial position, Vi is initial velocity, t is time, and a is acceleration.

Is what I am wondering is what is the basic equations for mechanics with a non zero jerk?

[snip]

So am I getting this correct, or am I missing something? What is the correct equation if anyone knows it. This is all I can come up with, without doing a differential equation or something, and I am not really sure how I would make it. I can not find this equation anywhere online, I cant google and find anything past basic physics 1 mechanics. thanks for any help

You probably won't see this equation terribly often online, because an acceleration that varies linearly with time (eg. constant Jerk) isn't a scenario with really much physical significance, since it corresponds to an unbounded time-varying force. As an exercise in calculus, it is somewhat interesting, but there isn't terribly much physics that you will be able to get out of this. Beyond constant acceleration, we don't usually have general equations of motion like what you describe except for a few very common cases, such as the harmonic oscillator [imath]\frac{d^2 x}{dt^2} = -kx[/imath]. Otherwise, you just get the acceleration from either Newton or Lagrange for mechanics, then solve the differential equation to get x(t). In a physics setting, I've rarely seen jerks ever come up as something of interest; I think engineers may use them on occasion for one reason or other.