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Lagrange Function for a certain problem

  • Thread starter headbam
  • Start date
  • #1
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Homework Statement



A particle of mass m is connected by a massless spring of force constant k and unstressed
length r0 to a point P that is moving along a horizontal circular path of radius a at a
uniform angular velocity ω. Verify the Lagrange-Function!

Homework Equations



Could there be a typing error in the book (the book provided the solution which can be seen in the file "function.png". My own solution just differs in the term with r and has 1/2*m*r^2*theta' instead of 1/2*m*r*theta' like shown in the book. However i think my solution is right or can anybody find a mistake?

The Attempt at a Solution



x[1](t):=a*cos(omega*t)#`this is the x-coordinate of P
y[1](t):=a*sin(omega*t)#`this is the y-coordinate of P
x[2](t):=x[1](t)+r(t)*cos(theta(t))#`this is the x-coordinate of m
y[2](t):=y[1](t)+r(t)*sin(theta(t))#`this is the y-coordinate of m
T := (1/2)*m*((diff(x[2](t), t))^2+(diff(y[2](t), t))^2)
V :=(1/2)*k*(r-r[0])^2
L=T-V

I attached a drawing of the exercise and two lagrange functions (from the book and my solution) and a Maple file for convenience.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Attachments

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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Your answer is almost certainly correct. That term in the books answer doesn't have consistent dimensions with the terms around it.
 
  • #3
2
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Ah yeah. I should have checked the dimensions as well! Thanks for the advice!
 

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