- #1
skrat
- 748
- 8
Homework Statement
I can't believe it how my brains stopped cooperating today.
We have the first ball with ##m_1 ## and ##v_1## and of course the second one with ##m_2## and velocity ##v_2##. Covariance matrix before the collision is ##M=
\begin{bmatrix}
\sigma _1^2 & 0\\
0& \sigma _2^2
\end{bmatrix}## . Calculate the covariance matrix after the elastic collision
Homework Equations
##{\vec x }'=\Phi {\vec x }## if ##\Phi ## is the transformational matrix and if ##{(xyz)}'## indicates the values after the collision.
The Attempt at a Solution
Now my idea was to move to the center of mass system but due to my brain blockage I am not able to find or to work with any given equation. -.-
This is wrong, and I can't find out why:
Lets use notation ##u## for the velocities in the center of mass system and let ##v_{CMS}## be the center of mass velocity. Than I guess ##u_1=v_1-v_{CMS}## and ##u_2=-v_2-v_{CMS}##.
Of course in center of mass system ##m_1u_1-m_2u_2=0## which leaves me with the most stupid thing ever, saying that ##v_{CMS}=\frac{m_1v_1+m_2v_2}{m_1-m_2}##.
Could somebody please help me a bit?