What does mg(theta) means in the equation of motion?

In summary, the equation of motion for an inverted pendulum attached in a cart with an external force U can be written as U - mg(theta1) - mg(theta2) = m*dv/dt. The θ's in this equation represent the small angles of the pendulum, allowing for approximations such as sin θ ≅ θ. More information is needed to fully understand the problem, and it is recommended to post in a relevant forum for further assistance.
  • #1
Aerodfocker
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In the case of inverted pendulum attached in a cart with external force U on it,

the equation of motion is like
U - mg(theta1) - mg(theta2) = m*dv/dt

I don't really understand the mg*theta part what does it mean ...should not be sine or cosine fn there with theta ?

can anyone give me some insight on this
thanks in advance ...really appreciate it.

p.s. I HAVE ATTACHED THE FULL QUESTION HERE AS WELL
 

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  • #2
It's just the equations of motion for the cart and the two pendulums. If you want to get more information you need to provide us with some first. E.g., we have to know what you are supposed to assume (e.g., are you supposed to use the least-action principle). Also it looks pretty much like a homework problem, which you should post in the corresponding subforum!
 
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  • #3
Aerodfocker said:
should not be sine or cosine fn there with theta ?

The problem statement says "small neighborhood of the equilibrium" which means the θ's are small so you can use approximations like sin θ ≅ θ.
 
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1. What is mg(theta) in the equation of motion?

mg(theta) is the component of the gravitational force acting on an object in motion, where m is the mass of the object and g is the acceleration due to gravity. Theta represents the angle between the direction of motion and the direction of the gravitational force.

2. How does mg(theta) affect the motion of an object?

The value of mg(theta) affects the acceleration of an object in motion. The larger the value, the greater the force acting on the object and the faster it will accelerate in the direction of the force. On the other hand, a smaller value of mg(theta) will result in a slower acceleration.

3. Can mg(theta) be negative in the equation of motion?

Yes, mg(theta) can be negative. This can occur when the angle theta is between 90 and 180 degrees, meaning that the gravitational force is acting in the opposite direction of the motion of the object. In this case, the acceleration will be negative, indicating that the object is slowing down.

4. Does mg(theta) change during the motion of an object?

No, mg(theta) does not change during the motion of an object, unless the value of either m or g changes. This is because the mass and acceleration due to gravity of an object typically remain constant throughout its motion.

5. How is mg(theta) related to the weight of an object?

mg(theta) is directly related to the weight of an object. The weight of an object is equal to the mass of the object multiplied by the acceleration due to gravity, which is represented by mg(theta) in the equation of motion.

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