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Minimisation Problem (Euler-Lagrange equation)

  • #1
36
0

Homework Statement


http://i.imgur.com/BV5gR8q.png

Homework Equations


d/dx ∂F/∂y'=∂F/∂y

The Attempt at a Solution


I have no problem with the first bit, but the second bit is where I get stuck. Since the question says the speed is proportional to distance, I have taken v(x)=cx where c is some constant of proportionality, then tried to proceed with solving the EL equation, however I end up with everything just being equal to 0 so I'm not sure how to proceed.

http://i.imgur.com/hDNPyG7.jpg
 

Answers and Replies

  • #2
Buzz Bloom
Gold Member
2,092
351
Hi Plaetean:

I think you forgot that y' is a function of x.

Your (d/dx) ∂F/dy' does not include any dy'/dx = y''.

Hope this helps.
Regards,
Buzz
 
  • #3
rude man
Homework Helper
Insights Author
Gold Member
7,627
714

Homework Statement


http://i.imgur.com/BV5gR8q.png

Homework Equations


d/dx ∂F/∂y'=∂F/∂y

The Attempt at a Solution


I have no problem with the first bit, but the second bit is where I get stuck. Since the question says the speed is proportional to distance, I have taken v(x)=cx where c is some constant of proportionality, then tried to proceed with solving the EL equation, however I end up with everything just being equal to 0 so I'm not sure how to proceed.

http://i.imgur.com/hDNPyG7.jpg
What does your Euler-Lagrange equation boil down to if F is not a function of y?
 

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