Lagrangian Mechanics with one constraint

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SUMMARY

The discussion revolves around solving a problem in Lagrangian Mechanics involving a box on a slab with a constraint. The user initially struggled to establish the relationship between the radial coordinate (r) and the angular coordinate (theta) to determine the normal force as a function of time. They attempted to use the Lagrangian equation but faced difficulties in deriving the correct expression. Ultimately, the user resolved the issue independently after receiving guidance from forum members.

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  • Understanding of Lagrangian Mechanics
  • Familiarity with constraints in mechanical systems
  • Knowledge of polar coordinates (r and theta)
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Natchanon
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Homework Statement


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r.PNG

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I'm supposed to find the normal force acting on the box by the slab as a function of time. The problem is I don't know what the constraint is. I can't find the relation between r and theta that adds the two up to zero.

Homework Equations


upload_2018-10-21_17-21-57.png

Lagrangian equation.

The Attempt at a Solution


I tried constraint f(r, theta , t) = theta and got lamda = mr (gcos(theta) + r theta(double dot) ) = mgrcos(theta) since omega is constant, but still couldn't get the right answer.
 

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Hello, and welcome to PF.

If you know ##r## and ##\theta## as functions of time, then I don't understand why you would need to bother with setting up the Lagrangian. Did you state the problem word-for-word as given to you?
 
TSny said:
Hello, and welcome to PF.

If you know ##r## and ##\theta## as functions of time, then I don't understand why you would need to bother with setting up the Lagrangian. Did you state the problem word-for-word as given to you?
Sorry for the late reply. I was able to figure it out. Thank you.
 

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