Now, we always need the relationship to the DCM. You've done this, you've seen all of the parameters, you're actually deriving that. Once you have the parameters, there's more algebra, but it's pretty straightforward, you can get CRPs, you can get MRPs, MRP formula starts to look a little bit more complicated in here. But actually, there is a really nice elegant compact location. So if I programing and I have a utility operation that are programming the map line of a python or something. It just takes a few lines of code and you can quickly code this up. This is how you go from MRP's to a DCM. The inrose mapping, like with CRP's they're no nice elegant direct way to do it a non singular way, that I've seen. People tend to just map him to all parameters. And then from all parameters is that one liner. Beta i over 1 + beta not. That's what gives you it. So we use shepherd's method, to get to all the parameters, and then you pull out these cotanions, not catanions. The CRPs, and MRPs. That's exactly the same thing. Now this. Will the property we discussed for CRPs. If C transposes is equal to my, the same thing as c of minus sigma. What do this mean? We discussed the same property with the CRP. So let's just review it here. It's the same mathematical property hold her for MRPs. >> Can you repeat the [INAUDIBLE]. >> We have the C matrix. So, the inverse over the direction cosine is the same thing as the transpose, right. I'm saying the transpose of C which is a function fo sigma is the same thing as the c matrix as the function of minus sigma, without the transpose. So, what was that mean about the MRPs including from N to B or B to N? I know that just makes it easier to go between the two because you don't have to do the [INAUDIBLE] >> So let's think of other angles again, because that's where this doesn't work. If I do you, pitch, roll, if I do 40, 40, 40, you, pitch, roll, no, can't use the same angles. No I think you can that still doesn't work. But let's say we do 30, 20, ten something like that just generally, right. That goes from n to p if I want to go from b back to n. I can just do minus 30, minus 20, minus ten. I don't end up with the same orientation. So you can't just take attitude restriction, throw on a negative side and now you go from n to b or b to n right,that works with omegas if I have the angular velocity of b relative to n and an angular velocity of n relative to b. All it takes is a negative sign, right, same thing with positions. I know the position of Charles relative to me if you want me relative to Charles this vector just gets reversed, that's it. Now these are not vectors, that's why this is cool, with vectors we expect that. Attitudes are not vector sets but it says Now, this matrix, sigma goes really from end to these, that's sigma b slash n, right, b relative to n goes to n2b, that's there. If you invert that, that means it's transposed, I get the attitude of n relative to b instead of b relative to n, I flipped, I've gone from one to the other originally. Now I'm going backwards. It means instead of doing a bunch complicated maths with, if you have to do it with angles that might good homework problem actually. To do this you'd have to go get the DCM of that orientation and then look at reverse you transpose it and you remember you have to take an inverse tangent and inverse cosine sine functions of certain elements. But because we transposed it, we're doing it on different metrics elements and you'll get different Euler angles. This is how you go back from B to N. There is a bunch of math. If you have any of these Rodrigues parameters, all I have to do is flip the sign. And that's really cool. It makes it act like a vector set but it's not a vector set. Please don't just add and subtract, right. We have to go through proper addition and subtraction properties. So that holds here actually, which is really nice.