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.
[1]
Hermann Bondi,et al.
The rigid body dynamics of unidirectional spin
,
1986,
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[2]
M Hubbard.
Human control of the skateboard.
,
1980,
Journal of biomechanics.
[3]
M. Hubbard,et al.
Spin reversal of the rattleback: theory and experiment
,
1988,
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.
[4]
A. S. Kuleshov.
MATHEMATICAL MODEL OF THE SKATEBOARD
,
2006
.
[5]
Mathematical model of a skateboard with one degree of freedom
,
2007
.
[6]
M. Hubbard.
Lateral Dynamics and Stability of the Skateboard
,
1979
.
[7]
R. Longman,et al.
On the dynamic behavior of the wobblestone
,
1981
.
[8]
On the Skateboard, Kinematics and Dynamics
,
2004
.