1,720,967 research outputs found
Existence of a periodic solution for superlinear second order ODEs
No full textWe prove a necessary and sufficient condition for the existence of a T-periodic solution for the time-periodic second order differential equation x ̈+f(t,x)+p(t,x,x ̇)=0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics
Penalization and Necessary Optimality Conditions for a Class of Nonsmooth Sweeping Processes
Full text linkIn this paper we derive necessary optimality conditions for a Mayer problem involving a controlled sweeping process characterized by a moving set which is merely locally prox-regular (not necessarily smooth) and satisfies a constraint qualification condition formulated exclusively in terms of its normal vectors. We employ a penalization method based on the distance from the moving constraint, which allows convergence estimates that are uniform with respect to the control and, moreover, the strong W1,2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}-convergence of the approximating solutions. An example of nonsmooth mechanics with finite degrees of freedom is presented
GAIT CONTROLLABILITY OF LENGTH-CHANGING SLENDER MICROSWIMMERS
No full textControllability results of four models of two-link microscale swimmers that are able to change the length of their links are obtained. The problems are formulated in the framework of geometric control theory, within which the notions of fiber, total, and gait controllability are presented, together with sufficient conditions for the latter two. The dynamics of a general two-link swimmer is described by resorting to resistive force theory and different mechanisms to produce a length-change in the links, namely, active deformation, a sliding hinge, growth at the tip, and telescopic links. Total controllability is proved via gait controllability in all four cases, and illustrated with the aid of numerical simulations
A vanishing-inertia analysis for finite-dimensional rate-independent systems with nonautonomous dissipation and an application to soft crawlers
No full textWe study the approximation of finite-dimensional rate-independent quasistatic systems, via a vanishing-inertia asymptotic analysis of dynamic evolutions. We prove the uniform convergence of dynamic solutions to a rate-independent one, employing the variational concept of energetic solution. Motivated by applications in soft locomotion, we allow time-dependence of the dissipation potential, and translation invariance of the potential energy
Generalizing the Poincaré–Miranda theorem: the avoiding cones condition
No full textAfter proposing a variant of the Poincaré–Bohl theorem, we extend the Poincaré– Miranda theorem in several directions, by introducing an avoiding cones condition. We are thus able to deal with functions defined on various types of convex domains, and situations where the topological degree may be different from ±1. An illustrative application is provided for the study of functionals having degenerate multi-saddle points
Coupling linearity and twist: an extension of the Poincaré–Birkhoff theorem for Hamiltonian systems
No full textWe provide an extension of the Poincaré-Birkhoff Theorem for systems coupling linear components with twisting components. Applications are given both to weakly coupled Hamiltonian systems where, e.g., a superlinear or sublinear behaviour is assumed in the nonlinear part of the coupling in order to recover the needed twist conditions, and to local perturbations of superintegrable systems, showing the survival of a number of periodic solutions from a lower-dimensional torus
Existence and regularity of solutions for an evolution model of perfectly plastic plates
No full textWe continue the study of a dynamic evolution model for perfectly plastic plates, recently derived in [19] from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model, and we discuss the regularity of the solutions thus obtained. In particular, we show that the first derivatives with respect to space of the stress tensor are locally square integrable
On the optimal control of rate-independent soft crawlers
Full text linkExistence of optimal solutions and necessary optimality conditions for a
controlled version of Moreau's sweeping process are derived. The control is a
measurable ingredient of the dynamics and the constraint set is a polyhedron.
The novelty consists in considering time periodic trajectories, adding the
requirement that the control have zero average, and considering an integral
functional that lacks weak semicontinuity. A model coming from the locomotion
of a soft-robotic crawler, that motivated our setting, is analysed in detail.
In obtaining necessary conditions, an improvement of the method of discrete
approximations is used
On the genesis of directional friction through bristle-like mediating elements
Full text linkWe propose an explanation of the genesis of directional dry friction, as emergent property of the oscillations produced in a bristle-like mediating element by the interaction with microscale fluctuations on the surface. Mathematically, we extend a convergence result by Mielke, for Prandtl–Tomlinson-like systems, considering also non-homothetic scalings of a wiggly potential. This allows us to apply the result to some simple mechanical models, that exemplify the interaction of a bristle with a surface having small fluctuations. We find that the resulting friction is the product of two factors: a geometric one, depending on the bristle angle and on the fluctuation profile, and a energetic one, proportional to the normal force exchanged between the bristle-like element and the surface. Finally, we apply our result to discuss the with the nap/against the nap asymmetry
Light-Responsive Hydrogel Microcrawlers, Powered and Steered with Spatially Homogeneous Illumination
No full textSub-millimeter untethered locomoting robots hold promise to radically change multiple areas of human activity such as microfabrication/assembly or health care. To overcome the associated hurdles of such a degree of robot miniaturization, radically new approaches are being adopted, often relying on soft actuating polymeric materials. Here, we present light-driven, crawling microrobots that locomote by a single degree of freedom actuation of their light-responsive tail section. The direction of locomotion is dictated by the robot body design and independent of the spatial modulation of the light stimuli, allowing simultaneous multidirectional motion of multiple robots. Moreover, we present a method for steering such robots by reversibly deforming their front section, using ultraviolet (UV) light as a trigger. The deformation dictates the robot locomotion, performing right- or left-hand turning when the UV is turned on or off respectively. The robots’ motion and navigation are not coupled to the position of the light sources, which enables simultaneous locomotion of multiple robots, steering of robots and brings about flexibility with the methods to deliver the light to the place of robot operation
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