A yoyo falls straight down unwinding as it goes, assume has inner radius a, outer radius b and Inertia I. What is the generalised coordinates and the lagrangian equation of motion?
L=T-U where T is kinetic energy and U is potential
The Attempt at a Solution
So i assumed that there are 2 parts of kinetic energy, downwards and rotational, the downwards:
1/2 m Y(dot)^2
1/2 I (Theta)(dot)^2 .
Potential is simply: mgy
This gives a lagrangian of L= 1/2 m Y(dot)^2 + 1/2 I (Theta)(dot)^2 - mgy
with general co-ords theta and Y, is this correct?