I'm having trouble understanding fictitious forces, so I looked up the wiki for it http://en.wikipedia.org/wiki/Fictitious_force. In the wiki entry, I have trouble understanding the mathematical derivation for fictitious forces in the early part of the article (along the mathematical derivation section, there's a mathematical model with a particle, an inertial frame of reference A, and a non-inertial frame of reference B, with displacement vectors written between those entities.) The equations for displacement vector between A, B, and the particle is given. Then the equations are differentiated twice to get the acceleration vector and multiplied by mass to get the force vector. The part I do not understand is the step where the author of the article writes Fb = Fa + F fictitious. I sort of understand how the author derived this mathematical statement, but I do not understand the meaning and implication of it. Does F fictitious represents Xab differentiated twice and multiplied by mass? If so, does that mean the fictitious force is actually force vector between inertial frame of reference A and non-inertial frame of reference B? I thought that the fictitious force is responsible for acceleration of mass in a non-inertial frame of reference. Please help.