No abstract

No 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.

Wheel slip model is an important aspect of vehicle driving stability and safety control. However, in most of the carriage movement models friction forces and wheel slip effect are being neglected. This paper raises the problem of wheel slip in dangerous driving and autonomous vehicles under critical driving modes, then tasks the modeling of movement of an individual vehicle is considered. These are two tasks of nonholonomic mechanics: 1) the movement of a wheelset without wheel slip (two disks freely mounted on an axis) along an inclined plane in the field of gravity, and 2) the movement of a flat wheel model, which, under certain assumptions, can be a four-wheeled carriage. In these tasks, in addition to the standard dynamics (continuous motion without wheel slip), critical situations can also be observed associated with wheel sleep and separation of wheels from plane.