Wow, that really helps. I forget what example it was when I was taking notes in class but I forgot with this approach you can kind of just use whichever axes you wish and it will still work.
That being said, this is what I have come up with.
T = 1/2 M \dot{x}^{2} + 1/2 m \dot{s}^{2} + 1/2 m...
I'm going to use the hoop on the non-moving ramp as my reference for this.
It has the equation of constraint being what describes the rolling without slipping, so
f = dx' - r d\theta = 0
f = \dot{x}' - r \dot{\theta} = 0
And y-ramp = 0.
And the generalized coordinates are x' and...
Homework Statement
A hoop of mass m and radius R rolls without slipping down an inclined plane of mass M, which makes an angle \alpha with the horizontal. Find the Lagrange equations and the integrals of the motion if the plane can slide without friction along a horizontal surface.
Homework...
Homework Statement
This is straight from the book.
A small block of mass m rests on the sloping side of a triangular block of mass M which itself rests on a horizontal table as shown in Fig. 4-50. Assuming all surfaces are frictionless, determine the force F that must be applied to M so...