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Lagrangian of system with circle and cube

  1. Nov 4, 2017 #1
    Hello. I have some problems with making Lagrangian. I need your advice.

    1. The problem statement, all variables and given/known data

    I have this situation:
    situation2.png

    Consider the circular path is intangible and without friction. I have to find Lagrangian for coordinates x and θ.

    2. Relevant equations

    L = U - V

    3. The attempt at a solution

    I know the result from a book:
    result.png

    The origin of the coordinate system is at the center of the initial position of the circular trajectory.

    I understand that the fist part is kinetic energy of big cube of mass M in coordinate x.The second part is kinetic energy of bead of mass m in a circle in coordinate x.
    I don't understand to third part. I think that the m (mass of bead) is missing there. If I will consider that m is there, it is kinetic energy of bead in coordinate θ.
    What is the poind of fourth part? I don't see it.
    The last part is potentional energy of bead, I understand.

    I wrote it there:
    lagrangian3.png


    So, could you tell me, if this Lagrangian right? And if it is not, how it has to look?
    Thank you.
     
  2. jcsd
  3. Nov 4, 2017 #2

    Orodruin

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    I suggest you write the position of the bead (both horizontally and vertically) as a function of the generalised coordinates. Differentiating it wrt time will give you the velocity.
     
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