Elliptical motion in polar coordinates

  • #1
lorenz0
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Homework Statement
Given that and , identify the trajectory and then find the position and velocity vectors in polar coordinates.
Relevant Equations
, ,
I think I have completed the exercise but since I have seldom used polar coordinates I would be grateful if someone would check out my work and tell me if I have done everything correctly. Thanks.
My solution follows.

Since it follows that the trajectory is an ellipse centered at the origin with axes and Now, and
so, since and we have that
 
Last edited:
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  • #2
Why do you have the squared tangent in the calculation? (OP was edited).
 
  • #3
dextercioby said:
Why do you have the squared tangent in the calculation?
Typo. Fixed, thanks.
 
  • #4
Please fix the whole calculation. There's no 2 anymore, since there's no square in the argument of (OP was again edited).
 
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  • #5
dextercioby said:
Please fix the whole calculation. There's no 2 anymore, since there's no square in the argument of .
Done.
 
  • #7
dextercioby said:
Much better.
Thanks!
 
  • #8
Sorry, there's an error in the calculation. The derivative of carries a minus.
 
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  • #9
dextercioby said:
Sorry, there's an error in the calculation. The derivative of carries a minus.
Corrected. Thanks again.
 
  • #10
Sorry, last check also in calculation. The 2 in the denominator stays there, if you use the 2 in the numerator to obtain the of double angle, right?
 
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  • #11
dextercioby said:
Sorry, last check also in calculation. The 2 in the denominator stays there, if you use the 2 in the numerator to obtain the of double angle, right?
You are right.
 
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