Accelerating reference frame

[MechatronO]

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 don't really understand it yet. No "loose" object are to be treated in the reference frame.

 

[A.T.]

You need to include inertial forces:
http://en.wikipedia.org/wiki/Fictitious_force#Mathematical_derivation_of_fictitious_forces

 

[MechatronO]

Aha. That was an interesting article.

The force observed from an arbitrary accelerating and rotating coordinatesystem is

Fb= Fa + F$_{fic}$

F$_{fic}$ = -(m$_{ab}$ + 2mƩv$_{j}$u'$_{j}$ + mƩx$_{j}$u´´$_{j}$)

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$_{ab}$ 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$_{ab}$ 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$_{ab}$ if the world of math smiles to me this time?