Accelerating reference frame

  1. 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.
     
  2. jcsd
  3. A.T.

    A.T. 6,186
    Gold Member

  4. 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?
     
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