Fd(L/2) cos(θ/2) = bv (L/2) cos(θ/2) = b * u cos(θ/2) * (L/2) cos(θ/2) = b * (L/2)^2 * cos(θ/2)^2. I see. I am taking the cosine of the direction of the damping velocity, not the door velocity. That's why cos(θ/2) appears twice multiplicatively.
Quite a complex diff eq to describe seemingly...
That was an interesting discussion - thanks for your help.
So my correct net torque equation should read :
(L/2) * [ mg sinθ - (bL/2)*θ' * cos(θ/2)] = (mL^2 / 3) * θ''
Is that correct?
It seems I'm still left with a second order nonlinear ODE, unfortunately, so this won't be as neat as I had...
I see what you're saying. So for determining the damping force bv, the v that I was using was of the door midpoint, and not the damper expansion velocity. What I need to do, then, is find the vector projection of the door midpoint velocity along the damper's direction, yes?
How does that...
I have defined v as the rate of expansion of the damper. I then convert the velocity of the point where the damper connects to the swinging door (xcom) to angular motion (v=r*omega). Does this make sense?
http://imgur.com/a/8QjoW
http://imgur.com/a/8QjoW
Hello-
I am trying to determine the dynamics of this linearly-damped hinge. Assuming that:
v(0) = 0
damping constant = b
door has mass = m
I was able to determine that:
∑Fx = -Fd * cos(45-θ/2) + Rx = m*dvx/dt
ΣFy = -Fd * sin(45-θ/2) - Fg +...