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Question: How to get equations of motion by applying hamilton's principle(or Eular-lagrange)?

Question:How to get equations of motion by applying hamilton's principle(or Eular-lagrange)?

Chirag 5 Maple
physics euler-lagrange
February 26 2015
1

Hi guys, 

       After my calculations, I got the Lagrange function having three gereralized co-ordinates namely u,v and w. Hence, according to theory it should give three equations of motion. 

      I have trouble finding equations of motion from following Lagrange function(L = T -U), Can anyone guide me with this?

      Moreover, kinetic energy and strain energy equations are in the form of double integral!! 
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