1. Not finding help here? Sign up for a free 30min 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!

Particle confined to move on the surface of sphere

  1. Aug 19, 2016 #1
    1. The problem statement, all variables and given/known data
    what will be Lagrange,s equation of motion for a particle confined to move on surface of sphere whose radius is expanding such that
    2. Relevant equations
    Euler-lagranges equation of motion
    d/dt(∂L/∂{dq/dt})-∂L/∂q=0

    3. The attempt at a solution
    Z=(R+R0e^at)cosθ
    X=(R+R0e^at)sinθcosΦ
    Y=(R+R0e^at)sinθsinΦ
    Lagrangian L=T-U
    T=1/2(mv^2)=1/2m{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}
    and
    U=mgz
    I just want to know whether i'm going on right track or not? and are the position coordinates right? Is the answer goes with the spherical pendulum?
     

    Attached Files:

  2. jcsd
  3. Aug 19, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello Kim, :welcome:

    I see nothing wrong with your approach. I take it you choose ##\theta## and ##\phi## as generalized coordinates.
    For ##R_0 = 0## you have the spherical pendulum case, so it's good to check with those expressions.
     
  4. Aug 19, 2016 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Are your "generalized coordinates" ##q## just ##\theta## and ##\phi##? If so, you need to express the Lagrangian in terms of them, so you need to figure out ##v^2## and ##U## in terms of ##\theta, \phi, \dot{\theta}, \dot{\phi}##.
     
  5. Aug 19, 2016 #4
    yeah i expressed v and U in terms of generalized coordinates, but i'm not sure if Φ varies (i mean equation of motion for Φ)
     
  6. Aug 20, 2016 #5
    and let me correct the problem-particle confined to move on the surface of sphere whose radius is expanding such a that R(t)=R+R0e^at
     
  7. Aug 20, 2016 #6

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    In general there is no a priori reason to assume anything about ##\phi##. There are two Lagrange differential equations, one for ##\theta## and one for ##\phi##. Write them down and see what they tell you.
     
  8. Aug 20, 2016 #7
    thanks for your view but are my x,y,z coordinates are correct if radius R is expanding such a that R(t)=R0e^at where t is time and a,R0 are constants? Was my approach correct as i described in- The attempt at a solution
     
  9. Aug 21, 2016 #8

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    It looks like the very beginning of a possibly correct approach, but is far from finished.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Particle confined to move on the surface of sphere
Loading...