1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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:

    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:

    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:

    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


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted