Related papers: Sliding Motions on SO(3), Sliding Subgroups
Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth system of ordinary differential equations. In this paper we quantitatively study the effects of small-amplitude, additive, white Gaussian noise on…
This is a survey of results on surfaces in noncommutative three-dimensional Lie groups obtained by using the Weierstrass (spinor) representation of surfaces. It is based on the talk given at the conference "Geometry related to the theory of…
We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…
When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order…
This paper proposes an event-triggered sliding mode control (SMC) scheme combined with a backstepping algorithm for control of 2-DOF humanoid's lower-limb powered by Series elastic actuator (SEA). First, the modelling process for the…
In the framework of Langevin dynamics, we demonstrate clear evidence of the peculiar quantized sliding state, previously found in a simple 1D boundary lubricated model [Phys. Rev. Lett. 97, 056101 (2006)], for a substantially less idealized…
Classical hydrodynamic models predict that infinite work is required to move a three-phase contact line, defined here as the line where a liquid/vapor interface intersects a solid surface. Assuming a slip boundary condition, in which the…
Recent highly idealized model studies of lubricated nanofriction for two crystalline sliding surfaces with an interposed thin solid crystalline lubricant layer showed that the overall relative velocity of the lubricant $v_{\rm lub} / v_{\rm…
We study the dynamics of a system of hard-core particles sliding downwards on a one dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the…
Robust finite-time feedback controller introduced for the second-order systems in [1] can be seen as a non-overshooting quasi-continuous sliding mode control. The paper proposes a regularization scheme to suppress inherent chattering due to…
Models of bipedal locomotion are hybrid, with a continuous component often generated by a Lagrangian plus actuators, and a discrete component where leg transfer takes place. The discrete component typically consists of a locally embedded…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we…
This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global…
In this paper, we study graphical conditions for structural controllability and accessibility of drifted bilinear systems over Lie groups. We consider a bilinear control system with drift and controlled terms that evolves over the special…
The PID controller is an elegant and versatile controller for set point tracking in double integrator systems of which mechanical systems evolving on Euclidean space constitute a large class. But since mechanical systems are typically…
The objective of this note is to share some reflections of the authors regarding the use of sliding mode designs in control systems. We believe the abundant, and ever increasing, appearance of this kind of works on our scientific…
We study a two-dimensional model for interacting colloidal particles which displays spontaneous clustering. Within this model we investigate the competition between the pinning to a periodic corrugation potential, and a sideways constant…
The idea of contact angle was generalized by using the principle of minimum total energy. The problems of the shape of the two-dimensional sessile drop and the drop on an inclined surface are considered. The differential equations…
The Lie-group approach was applied to determine symmetries of the third-order non-linear equation formulated for description of shear elastic disturbances in soft solids. Invariant solutions to this equation are derived and it turned out…