I'm attempting to build a line follower robot and I'm currently in the process of building appropriate models. For the control system I need to define a coordinate system. The most convinient coordinate system from many point of views would be a coordinate system that moves along and changes direction with the robot, thus a rotating and accelerating reference frame. The question is if calculations regarding acceleration still would be valid if they are carried out in the same way as in a fixed reference frame. The calculations to be carried out are: ƩM = Jω' - Angular acceleration related to net torque applied ƩF = ma - Acceleration of center of gravity related to net force applied I've glanced some about information regarding the coriolis effect but I dont really understand it yet. No "loose" object are to be treated in the reference frame.
You need to include inertial forces: http://en.wikipedia.org/wiki/Fictitious_force#Mathematical_derivation_of_fictitious_forces
Aha. That was an interesting article. The force observed from an arbitrary accelerating and rotating coordinatesystem is Fb= Fa + F[itex]_{fic}[/itex] F[itex]_{fic}[/itex] = -(m[itex]_{ab}[/itex] + 2mƩv[itex]_{j}[/itex]u'[itex]_{j}[/itex] + mƩx[itex]_{j}[/itex]u´´[itex]_{j}[/itex]) Fb is the appearent force that an observer in a rotating reference frame would think is acting on an object, while F is the "real" force an observer in an inertial reference frame would see and Ffic is the fictional force coming from the movements of the ref. system and m[itex]_{ab}[/itex] is the acceleration of the ref. system. I however want a coordinatsystem that is fixed both in position and angle to the robot at a point on the robot which defines position [0,0,0]. The position and velocity in its "own" coordinatesystem would thus be 0. Will this zero all terms in the Ffic and leave Fb = F - m[itex]_{ab}[/itex] in this particular case? As the robot would see the acceleration and in combination the force "on itself" in this system as zero we would get back F = m[itex]_{ab}[/itex] if the world of math smiles to me this time?