Vertical Bicycle Model of Vehicle with Dry Friction

Abstract

The motion of a vertically positioned bicycle is considered when a horizontal control force, which maybe both internal and external in relation to the bicycle, is applied to its pedal. Tangential forces of dryfriction obeying the Euler { Coulomb law act at points of contact of the wheels with the horizontal supportplane. The constraint at the points of contact of the wheels with the support is assumed to be unilateral.The problem of determining the acceleration of the centre of mass of the bicycle and the realized motionsof its wheels (with or without slip, and with or without detachment) with dierent values of the design parameters and control force is solved. This approach is usefull for control of vehicle and optimization of its dynamical parameters. Cases of non-uniqueness of motion the Painleve paradox are found.