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!

Yet another Lagrangian problem. Motion in a cone

  1. Nov 16, 2011 #1
    Man I hate to make two post in one day but I am really stuck!

    1. The problem statement, all variables and given/known data
    A particle slides on the inside surface if a frictionless cone. The cone is fixed with its tip on the ground and its axis vertical. The half angle of the tip is α. Let r be the distance from the particle to the axis, and let θ be the angle around the cone.

    1. Find the equations of motion.
    2. If the particle moves in a circle of radius r_0, what is the frequenct of this motion ω?
    3. If the particle is perturbed slightly from the circular motion, what is the frequency of oscillations about the radius r_0?

    2. Relevant equations
    Lagrangian and Lagranges Equations


    3. The attempt at a solution
    If need be, I will draw a picture and upload it so the relations used are more obvious.
    First thing is first, is my Lagrangian correct? (I made an image in MathType, its easier for me.)
    [PLAIN]http://img197.imageshack.us/img197/9997/lag1.gif [Broken]

    I do not think this is correct because I am not getting oscillatory motion for theta when I solve!

    EDIT: Oh! I forgot to mention! 'l' is the distance on the side of the cone from the point to where the particle is. I do not know how to include this in the lagrangian!
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 16, 2011 #2
    Okay so I realized I didn't include [itex]\dot{z}[/itex]! After including that, I have...
    [itex]L=\frac{1}{2}m \left( \frac{\dot{r}^2}{sin^2σ}+r^2 \dot{θ}^2 \right)-\frac{mgr}{tanα}[/itex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Yet another Lagrangian problem. Motion in a cone
  1. Lagrangian problem (Replies: 1)

  2. Problem on Lagrangian (Replies: 5)

Loading...