I have an equation which is the Rodrigues Rotation formula but rewritten different.
Where $p,w,t,r,v,q,s$ are all the unknown variables and $R,n$ are known. For every positive value $n$ there is a known value for $R$, therefore one can obtain the 7 equations needed to solve for the 7 unknowns. But of course, due to the similarities between these 7 equations I wonder if there’s is a better and easier way to solve for the unknowns. Also, what if instead of 7 variables there are 14, or 21, or any multiple of 7 variables in the same conditions, where for any positive value $n$ there is a known value $R$.
Another case I need to solve is for 8 unknowns, where the only difference is the following
Where the same question applies to this case, and what would happen if the unknowns would double or triple in this case ?