Rotating Bodies Around Origin: Analyzing Motion & Dynamics

[Silviu]

Homework Statement

Hello! I have 2 bodies initially at rest, of equal masses with the distance between them a and coordinates $(a cos(\theta),a sin(\theta))$ and $(-a cos(\theta),-a sin(\theta))$. If we denote $a_x$ and $a_y$ the horizontal and vertical distance between them they satisfy a relationship which gets reduced to what I write in 3. Show that they rotate around the origin (keeping the distance between them fixed)

Homework Equations

The Attempt at a Solution

$\frac{d^2 a_x}{dt^2} = A(1+i)\omega^2e^{-i\omega t}$ and $\frac{d^2 a_y}{dt^2} = A(-1+i)\omega^2e^{-i\omega t}$. So I get $a_x = A(1+i)e^{-i \omega t}+Bt+D$ and $a_y = A(-1+i)e^{-i \omega t}+Et+F$. If I put the condition to be stationary in the beginning (t=0), I get $B=A(1+i)$ and $E=A(-1+i)$ But I am kinda stuck. What should I do from here?

 

[BvU]

Hi,
Where on Earth does your first = in the attempt come from ? There is no mention of $t$ at all in your problem statement !?

they satisfy a relationship which gets reduced to what I write in 3

Which one (what relationship) ? Says who ?

 

[Silviu]

Hi,
Where on Earth does your first = in the attempt come from ? There is no mention of $t$ at all in your problem statement !?
Which one (what relationship) ? Says who ?

The whole statement is long so I just put the last version of it. It is given and equality that involves some things defined in the book so I just put the point where I got stuck. t is the time

 

[haruspex]

The whole statement is long so I just put the last version of it. It is given and equality that involves some things defined in the book so I just put the point where I got stuck. t is the time

Ok, but it would help if you were to make a three way distinction: the part of the question you are trying to solve, what you have already established from earlier parts, and your attempt at this part.
I assume that your two expressions for the accelerations fall into the middle section, but I cannot understand how they can be right. The resulting accelerations will be complex. Shouldn't they be real? If it is reasonable that they are complex you will nee to post much more of the given question.

distance between them a

The distance between the coordinates you quote is 2a.