In the discussion for equation for motion for "rolling disk inside a ring" in webpage http://demonstrations.wolfram.com/DiskRollingInsideARotatingRing/ by Mr. Erik Mahieu Lagrangian for the system is not getting displayed. I tried getting it. First, thing I felt that the first equation of motion should r^-2 instead of r^-1. By reverse engineering and my own knowledge I could get the Lagrangian as (K - V) where

K = (1/2  I_1  ?'^2) +(1/2  I_2 ?'^2) + (1/2  m_2 (R-r)^2  ?'^2 ) + (m_2 * (R-r)  )(Cos ?) ?' (R ?' )
      + (1/2 (m_1 + m_2 ) R^2 ?'^2)
V = m_1 g R + m_2 g (R-r)(1-Cos ?)

But the problem is first equation of motion should have the term

(m_2 (R-r)  )(Sin ?) ?' (R ?' )

I am not able to get the clear picture and complete physical interpretation of the last two terms of K. I will be grateful if I can get the Lagrange of the system be displayed with a bit of explanation. Regards, Ravi Shankar Gautam

Attachments:

lagrange.png

lagrange_missing...png