We know that spiral galaxies spin in a way such that we have to assume that dark matter is responsible for the extra mass required to do so.
My question is, can Lagrangian points (L1 and L2) be used to describe a galaxy's rotation instead?
Can we explain that objects far away from the center of the galaxy have higher velocity because they are at the L2 Lagrangian point of a Lagrangian system which consists of a) the galaxy's super massive black hole at its center, b) a part of its spiral arm c) the far away object in question?
(I'm a computer engineer interested in physics. Please excuse my ignorance)