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Math Help - Find r(dot)

  1. #1
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    Find r(dot)

    Can anyone show me how to find r(dot) of the following vector?

    r = <x,y> + (lm)/(m+n)<cos(theta),sin(theta)>
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  2. #2
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    Re: Find r(dot)

    Quote Originally Posted by mezy View Post
    Can anyone show me how to find r(dot) of the following vector?
    r = <x,y> + (lm)/(m+n)<\cos(\theta),\sin(\theta)>
    You need to be more forthcoming about this post.
    What does r(dot) mean?
    In the definition of r what are the variables?
    What are the constants?
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  3. #3
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    Re: Find r(dot)

    Quote Originally Posted by Plato View Post
    You need to be more forthcoming about this post.
    What does r(dot) mean?
    In the definition of r what are the variables?
    What are the constants?
    Sorry about that. Here is the complete question:

    Two point masses m_{1} and m_{2} are joint together by a rigid light rod of lenth \ell. If the rod move on a vertical plane under the action of the earth's gravitational field only, show that the path of the center of mass is a parabola and the rod rotates about the center of mass at a uniform angular velocity.

    The given information I have is:

    \vec{r_{1}} = <x,y> + \displaystyle{\frac{\ell m_{1}}{m_{1}+m_{2}}} <cos (\theta),sin (\theta)>

    and

    \vec{r_{2}} = <x,y> - \displaystyle{\frac{\ell m_{2}}{m_{1}+{m_{2}}} <cos (\theta),sin (\theta)>

    Prove that \theta is cyclic.

    To do this, the first step is to find \dot{\vec{r_{1}}} and \dot{\vec{r_{2}}} and use them to find the Euler-Lagrangian equation.

    I hope that's a little more specific. I just need help finding \dot{\vec{r_{1}}} .

    Thanks!
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  4. #4
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    Re: Find r(dot)

    Quote Originally Posted by mezy View Post
    Sorry about that. Here is the complete question:

    Two point masses m_{1} and m_{2} are joint together by a rigid light rod of lenth \ell. If the rod move on a vertical plane under the action of the earth's gravitational field only, show that the path of the center of mass is a parabola and the rod rotates about the center of mass at a uniform angular velocity.

    The given information I have is:

    \vec{r_{1}} = <x,y> + \displaystyle{\frac{\ell m_{1}}{m_{1}+m_{2}}} <cos (\theta),sin (\theta)>

    and

    \vec{r_{2}} = <x,y> - \displaystyle{\frac{\ell m_{2}}{m_{1}+{m_{2}}} <cos (\theta),sin (\theta)>

    Prove that \theta is cyclic.

    To do this, the first step is to find \dot{\vec{r_{1}}} and \dot{\vec{r_{2}}} and use them to find the Euler-Lagrangian equation.

    I hope that's a little more specific. I just need help finding \dot{\vec{r_{1}}} .

    Thanks!
    r = <x,y> +k<cosw,sinw>
    dr/dt = <dx/dt,dy/dt> +k<-sinw(dw/dt),cosw(dw/dt)>
    = <dx/dt,dy/dt> +k(dw/dt)<-sinw,cosw)>

    assuming k constant. otherwise you have to differentiate that too. d/dt(k<x,y>=dk/dt<x,y> +k<dx/dt,dy/dt>
    Last edited by Hartlw; October 20th 2011 at 06:23 PM.
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