Inserted mass on a rotating ring, problem with solution interpretation

In summary, the conversation is about a problem with a system involving a differential equation with three solutions depending on ω. The issue is that one of the solutions, θ=θocosh(Ωt), grows exponentially when t is increased, which is not expected for small oscillations. The possibility of an unstable equilibrium is also brought up.
  • #1
albandres
1
0

Homework Statement



Its about a system like in picture. I have it solved alredy BUT I still have a problem
After getting the dynamic equation by Newtonian and Lagrangian methods I solved one of them making the hipótesis of Little oscillations. This diferential equation has three solutions depending on ω.

http://www.acienciasgalilei.com/public/forobb/galeria/tmp4/a44be89a0d.png [Broken]

Homework Equations



The problem is that one of them is: θ=θocosh(Ωt) but when we increase t, θ grows exponetially till the infinite! How can this be posible if this is a solution only suitable for small oscillations?

Thanks!

PD: sorry about my english (Im spanish, and I am very tired now)
 
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  • #2
ola albandres! welcome to pf! :smile:
albandres said:
Its about a system like in picture.

The problem is that one of them is: θ=θocosh(Ωt) but when we increase t, θ grows exponetially till the infinite! How can this be posible if this is a solution only suitable for small oscillations?

erm :redface:

no picture! :biggrin:

it's difficult to say without knowing the set-up, but does this solution represent an unstable equilibrium?
 

1. What is the purpose of inserted mass on a rotating ring?

The inserted mass on a rotating ring is used to simulate the effect of an object being placed in orbit around a larger rotating body, such as a planet or a star. It allows scientists to study the dynamics and behavior of the system without the need for a physical object.

2. How is inserted mass calculated on a rotating ring?

The inserted mass is typically calculated using the formula m = ω^2r/G, where m is the inserted mass, ω is the angular velocity of the rotating ring, r is the radius of the ring, and G is the gravitational constant.

3. What are the limitations of using inserted mass on a rotating ring?

One limitation is that the inserted mass only provides an approximation of the effects of a real object in orbit. It does not take into account factors such as the object's mass distribution or the gravitational influence of other bodies in the system.

Another limitation is that the solution interpretation may be complex and require advanced mathematical and computational techniques, making it difficult to draw clear conclusions.

4. How can the results from inserted mass experiments be applied to real-life scenarios?

The results from inserted mass experiments can help scientists better understand and predict the behavior of objects in orbit, such as satellites and planets. This information can be used to improve space missions and develop more accurate models of our solar system.

5. What other factors should be considered when using inserted mass on a rotating ring?

In addition to the inserted mass, other factors such as the ring's material, shape, and rotation speed can also affect the system's dynamics. Scientists must carefully consider and control these variables in order to accurately interpret the results of their experiments.

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