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Energy dissipation and hysteresis cycles in pre-sliding transients of kinetic friction

Michael Ruderman (2023)

Applications of Mathematics

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...

Entropy and complexity of a path in sub-riemannian geometry

Frédéric Jean (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an ε -neighborhood of the path,...

Entropy and complexity of a path in sub-Riemannian geometry

Frédéric Jean (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...

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