zoom1
- 63
- 0
Didn't get this equation which is written for the pendulum part of the cart.
Must be easy but couldn't get it.
Understanding the Pendulum Dynamics Equation for a Cart
- Thread starter zoom1
- Start date
-
- Tags
- Dynamics
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
3 replies · 2K views
Didn't get this equation which is written for the pendulum part of the cart.
Must be easy but couldn't get it.
Discussion
- 6,999
- 299
It is just "force = mass x acceleration" in the x direction, for the center of mass of the rod. (The length of rod isn't shown on your diagram, but if the equation is correct it is 2l, not l).
The ##\ddot\theta## term is from the tangential acceleration of the rod.
The ##\dot\theta^2## term is the from the radial (centripetal) acceleration.
The ##\ddot\theta## term is from the tangential acceleration of the rod.
The ##\dot\theta^2## term is the from the radial (centripetal) acceleration.
zoom1
- 63
- 0
AlephZero said:
It's a little clearer now, but didn't understand the centripetal force component.
Isn't it
- 6,999
- 299
Yes.
You also know ##v = \omega r## and ##\omega = \dot\theta##
The centripetal force is radial (along the length of the rod), but the equation is for the component of the force in the X direction.
You also know ##v = \omega r## and ##\omega = \dot\theta##
The centripetal force is radial (along the length of the rod), but the equation is for the component of the force in the X direction.