Two different ways to model friction

frictiondifference.mo

// New, in https://github.com/dzimmer/ZimmersModelicaTutorial/blob/master/Tutorial2015/BaseComponents/Friction/IdealDryFriction.mo
  free = false;
  f0 = R;
  f0_max = S;
  // velocity and acceleration of flanges
  v_relfric = der(-s_rel);
  a_relfric = der(v_relfric);
  // Friction force
  -f = if locked then sa * unitForce else if startForward then R else if startBackward then -R else if pre(mode) == Forward then R else -R;

// Old, from draft
  v = der(flange_a.s - flange_b.s);
  flange_a.f + flange_b.f = 0;
  a = der(v);
  flange_a.f = if Forward then R else if Backward then -R else if StartForw then R else if StartBack then -R else fR;
  Forward = initial() and v > 0 or pre(StartForw) and v > 0 or pre(Forward) and not v <= 0;
  Backward = initial() and v < 0 or pre(StartBack) and v < 0 or pre(Backward) and not v >= 0;
  StartForw = pre(Stiction) and fR > S or pre(StartForw) and not (v > 0 or a <= 0 and not v > 0);
  StartBack = pre(Stiction) and fR < (-S) or pre(StartBack) and not (v < 0 or a >= 0 and not v < 0);
  Stiction = not (Forward or Backward or StartForw or StartBack);
  0 = if Stiction or initial() then One * a else fR;
  when Stiction and not initial() then
    reinit(v, 0);
  end when;

These are Modelica equations from IdealDryFriction, part of a Modelica tutorial that will be given at the Modelica conference.