rotation_table.md

@@ -49,3 +49,18 @@ Next, we have to find a vector ![alt text](http://mathurl.com/jm7yc4a.png). We k
 ![alt text](http://mathurl.com/zjeuyqv.png)
 
 As we can see all eigenvectors of ![alt text](http://mathurl.com/5unln6.png) can satisfy this. We calculate them and select the one corresponding to the smallest eigenvalue.
+
+
+### Translation vector
+
+The translation vector ![alt text](http://mathurl.com/hrfjerk.png) must satisfy that it remain same when transformed. So we get:
+
+![alt text](http://mathurl.com/hz8h7pf.png)
+
+However, this equation have multiple solution in a 3D space. So we must add an other condition to this to clarify the solution. We know that both origins are rotating in a plane with normal vector ![alt text](http://mathurl.com/jm7yc4a.png) from previous. Moreover, the normal vector must be perpendicular with the vector ![alt text](http://mathurl.com/hrfjerk.png). We can add a following condition:
+
+![alt text](http://mathurl.com/hb4t2zq.png)
+
+Now, we are able to write it as a matrix equation:
+ 
+![alt text](http://mathurl.com/jk4j7dp.png)