DYNAMICS AND SIMULATION OF THE SIMPLEST MODEL OF A SKATEBOARD

Department of Mechanics and MathematicsMoscow State UniversityRussian Federationkuleshov@mech.math.msu.suAbstractIn the present paper analysis and simulation are per-formedforthe simplest modelof a skateboard. We sup-pose the skateboard is uncontrollable. The equations ofmotionof the model are derivedandtheir stability anal-ysis is fulfilled.Key wordsskateboard; nonholonomic constraints; integrability;normal form; simulation1 IntroductionNowadays skateboarding that is rider’s skill, has be-come one of the most popular kind of sport. Neverthe-less serious researchesconcerningdynamicsand stabil-ity of a skateboard are almost absent. At the late 70th -early 80th of the last century Mont Hubbard [1; 2] pro-posedthe two mathematicalmodelsdescribingmotionsof a skateboard in the presence of a rider. To derive theequations of motion he used the principal theorems ofdynamics. In our paper we give the further develop-ment of the models proposed by Hubbard.