the small one would kinda be orbiting around the big one, but ideally it should stay pretty much on top of it. this is kind of like a inverted pendulum problem.
so for the small wheel, the transitional motion would be
\frac{1}{2}m((R+r)\dot{θ}cosθ)^2.
you are missing the square on the...
the wheel on the bottom does not slide. the small one is actually a motor that turns the big one. so they are stuck together.
I don't get what you mean "and write down the position of the small one relative to the big one. Then just add them to get the position w.r.t to the ground, and use...
Homework Statement
Here's the free body diagram with variables.
I am looking for the lagrangian mechanics equation.
M is mass of the bottom wheel.
m is the mass of the top wheel.
R is the radius of the bottom wheel.
r is the radius of the top wheel.
θ_{1} is the angle from vertical of...
I understand Fl=I\ddot{θ} but where is the 1/2 from?
oh so you're saying this would be substituted into the main force equation, which would be how gravity is accounted for?
since the force acted on by gravity going down the rod is mgcosθ, the horizontal force on the cart would be...
I am looking at this equation, but you mentioned that the centrifugal force and the torque is due to gravity, but how come there's no mg or g term in the equation?
ok so i drew my own and actually figured out where his calculations come from, but i am not sure if i drew the forces right, and I am wondering why the website is missing the 1/3 from the inertia of a rod rotating on its end. I also don't know why my signs are different.
(i left out the trig...
Isn't the torque from the second term be due to gravity, while the centrifugal force from the third term also due to gravity. So gravity is acting on both? I am having trouble creating my own free-body diagram for inverted pendulum on a cart, since i don't even really get this example.
In the equation i posted he's calculating force, he doesn't use I until later in the equations in the website.
so you're saying \frac{1}{2}I\dot{\theta}^2 comes from angular acceleration due to gravity? but then shouldn't the arrow be pointed in the bottom left direction?
Homework Statement
I am trying to understand where the forces in the inverted pendulum comes from starting with this horizontal force equation:
http://www.engin.umich.edu/group/ctm/examples/pend/inveq2.GIF
It is associated with this picture...