During week 8 I added several methods which calculate transformation equations for some specific situation. We’ve finished step, where transformation equations are obtained for rotation, translation, and changing the type of coordinate system. This all transitions are handled in vector module. We’ve also prepared the method for composition of any two kind of transformations, because coordinate system can be rotated and translated at the same time.

My current task is to use already added methods in CoordSys3D constructor. We’re going to define transformation equations similarly to rotation matrix. We will also add some method like orient_new to linking two coordinate system, where one of them is parent coordinate system.

Including also inverse transformation equations allows us to easily express vectors and scalars from new coordinate system in terms of old coordinate system. Inverse transformation equations has also another one big advantage. We can always connect our coordinate system to Cartesian system. So, if we have two independent coordinate system defined by some transformation equations, we can recalculate some quantity to Cartesian one and then recalculate to the second coordinate system. This mechanism could be implemented in express function in sympy/vector/functions.py file.