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Polar coordinates and kinematics

  • Thread starter Telemachus
  • Start date
832
30
1. Homework Statement
I've got some trouble and doubts with polar coordinates. I have this exercise, with a rocket going upwards, with a given acceleration. So I need to find the polar equation for the given situation for the position, the velocity and the acceleration. How should I proceed? I mean, I know I must find an equation that describes the path for r(t) in the polar form, but I'm not sure on how the acceleration fit on this.

attachment.php?attachmentid=28831&stc=1&d=1286321434.png


The distance between the origin and the rocket "D" is given by the problem data.
2. Homework Equations
[tex]r(t)=r\vec{e_r}[/tex]
[tex]v(t)=\dot r\vec{e_r}+r\dot \theta\vec{e_{\theta}}[/tex]
[tex]a(t)=(\ddot r-r\dot \theta^2)\vec{e_r}+(r\ddot \theta+2 \dot r \dot \theta)\vec{e_{\theta}}[/tex]

I think that [tex]r(t)[/tex] could be: [tex]r(t)=\sec \theta \vec{e_r}[/tex], but then I don't know how to work with the acceleration on the radial direction, or over the angle direction neither. Should I use trigonometry for this?
 

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Last edited:
832
30
I've tried this way, but it doesn't looks fine really

[tex]a=k[/tex], [tex]s=kt[/tex] [tex]x=\displaystyle\frac{k}{2}t^2[/tex]

Then the radial speed:
[tex]\dot r=s \cos \theta=kt \cos \theta[/tex]

And the angular speed:
[tex]\dot \theta=s \sin \theta=kt \sin \theta[/tex]

I think that the equation for r(t) should be [tex]\vec{r(t)}=\sec \theta \hat{e_r}[/tex]. But I don't know how to work with it.

[tex]\dot r=v(t)=\dot r\vec{e_r}+r\dot \theta\vec{e_{\theta}}[/tex]
[tex]\dot r=\sec r \tan r\hat{e_r}+\sec r \dot \theta \hat{e_{\theta}}[/tex]

I don't know how to determine the radial speed and the angular speed, considering the acceleration, and I think what I've done doesn't make any sense.

Any help please?
Bye there.
 

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