Drifting on plane curves

Abstract The paper describes a particular model of a drifting car. We analyse drifting along an arbitrary plane curve and conclude that, depending on the desired level of smoothness of motion, either that drifting is always possible under mild conditions, or if the smoother solution is desired, drifting is possible, if the curvature $$\kappa $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>κ</mml:mi> </mml:math> of the curve is not changing to rapidly in a certain sense. We introduce the notion of a wide function and the conclusion is that if the function $$\frac{1}{2\kappa }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>κ</mml:mi> </mml:mrow> </mml:mfrac> </mml:math> is a wide function, then smooth drifting along the curve is possible. We give explicit examples of drifting along various curves.