A discretization of the nonholonomic Chaplygin sphere problem.
Application of differential equations
Ehresmann Connection in the Geometry of Nonholonomic Systems
Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction
The problem of transient hysteresis cycles induced by the pre-sliding kinetic friction is relevant for analyzing the system dynamics, e.g., of micro- and nano-positioning instruments and devices and their controlled operation. The associated energy dissipation and consequent convergence of the state trajectories occur due to the structural hysteresis damping of contact surface asperities during reversals, and it is neither exponential (i.e., viscous type) nor finite-time (i.e., Coulomb type). In...
Isomorphism and Hamilton representation of some nonholonomic systems.
On the analytic non-integrability of the Rattleback problem
We establish the analytic non-integrability of the nonholonomic ellipsoidal rattleback model for a large class of parameter values. Our approach is based on the study of the monodromy group of the normal variational equations around a particular orbit. The imbedding of the equations of the heavy rigid body into the rattleback model is discussed.
Phase space of rolling solutions of the tippe top.