How do you convert from LA to CI system using right ascension and declination?

[G4CKT]

Homework Statement

I was given a question to transform the LA system to the CI system. (Local astronomic and Conventional Inertial)

Homework Equations

r^LA=P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P*r^CL

The Attempt at a Solution

I attempted this on MATLAB but I used the wrong rotation and got the question wrong so I was wondering if anyone knew how to convert LA -> CI

 

[HallsofIvy]

I see "LA" on the left side of the equation but I see no "CI". Was the "CL" on the right supposed to be "CI"?

If so, first divide both sides by all the numbers on the right to get
$$r^{CI}= \frac{r^{LA}}{P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P}$$

Now, take the logarithm of both sides (it doesn't matter what base)
$$CI log(r)= LA log(r)- log(P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P)$$
Finally, divide both sides by log(r) to get
$$CI= LA- \frac{log(P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P)}{log(r)}$$

 

[G4CKT]

I see "LA" on the left side of the equation but I see no "CI". Was the "CL" on the right supposed to be "CI"?

If so, first divide both sides by all the numbers on the right to get
$$r^{CI}= \frac{r^{LA}}{P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P}$$

Now, take the logarithm of both sides (it doesn't matter what base)
$$CI log(r)= LA log(r)- log(P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P)$$
Finally, divide both sides by log(r) to get
$$CI= LA- \frac{log(P1*R2(90-Ф)*R3(Λ)*R2(-xp)*R1(-yp)*R3(GAST)*N*P)}{log(r)}$$

Yes, that is correct I was confusing myself, sorry xD.

I have another question in order to find the CI using right ascension and declination. How would I be able to compute that?

Thanks!

Maybe I should be in the astronomy section xD