The streetboard rider: an appealing problem in non-holonomic mechanics

摘要

This paper enlarges the reservoir of solved tutor problems in non-holonomic mechanics at the undergraduate level of physics education. Unlike other, rather artificial, solved problems typically used, the streetboard-rider locomotion problem presented here represents an appealing contemporary real-world problem with interesting applications in a popular sport and in robotics. In this paper, the streetboard motion is discussed from the physical point of view. We show that the interesting snake-like motion performed by streetboard riders stems from its non-holonomic nature. The related non-holonomic constraints are derived and the problem of the mechanical system subjected to these non-holonomic constraints is solved using methods appropriate to the undergraduate university level. The analytical solution for the circular motion and the numerical solution for the general motion are obtained, the physical meaning of the derived constrained forces is investigated and the results are discussed with respect to observed streetboard-rider locomotion. The brief outline of the paper can be used as a demonstration example in non-holonomic mechanics lessons, while the paper itself establishes an original undergraduate computational student project in theoretical mechanics.