arXiv subjects

Stefano Pasquero

Publications and source records attributed to Stefano Pasquero.

7 recordsLinked to original sources

arXiv2026

Notes on a paper by F. Génot and B. Brogliato on the Painlevé paradox

We reconsider the analysis of the Classical Painlevé Problem developed by F. Génot and B. Brogliato ([1] New results on Painlevé paradoxes. - European Journal of Mechanics-A/Solids, 18(4):653{677, 1999), focusing on the consistency of their results with Galilean invariance. We show that certain conclusions concerning the dynamical evolution of the mechanical system are not invariant under changes of Galilean observer and therefore cannot, in their present form, be interpreted as intrinsic properties of the system. In particular, we show that the classi?cation of motion states depends on the observer through the velocity{dependent characterization of the frictional constraint, and we trace the origin of this dependence to the Galilean velocity-addition theorem. We present and discuss possible reformulations of the model aimed at restoring observer-invariant descriptions of the problem.

math-ph↗

arXiv2026

An alternative approach to the Painlevé paradox through constitutive characterization of constraints in impulsive Mechanics

We frame the Painlevè mechanical system, which has been extensively studied because of the paradox it generates, within the class of Regular Geometric Impulsive Mechanical Systems (RGIMS), by modeling it as a mechanical system subject to a rough unilateral positional constraint $\cal{S}$, where friction is represented by an instantaneous kinetic constraint $\cal{B}$, internal to $\cal{S}$ and of impulsive nature. The evolution of the system is therefore determined by the choice of a constitutive characterization for these constraints, a choice that restores mechanical determinism and eliminates any paradoxical aspects of the system's behavior, in agreement with experimental evidence. It is shown that, similarly to what occurs in general non ideal impulsive systems, the choice of a constitutive characterization of the constraint system depends on the determination of two numerical coefficients $σ$ and $β$, which depend on the kinematic and mass-related data of the system, and possibly also on physical quantities not strictly of a mechanical nature, such as material properties. The simplicity of the model also allows for a straightforward experimental analysis of the system's behavior and for the experimental determination of the values of these coefficients.

math-ph↗

arXiv2026

Geometric characterization of frictional impacts by means of breakable kinetic constraints

In the context of geometric Impulsive Mechanics of systems with a finite number of degrees of freedom, we model the roughness of a unilateral constraint ${\mathcal S\/}$ by introducing a suitable instantaneous kinetic constraint ${\mathcal B\/}\subset {\mathcal S\/}$. A constitutive characterization of ${\mathcal B\/}$ based only on the geometric properties of the setup and on the dry friction laws can then be introduced to model the frictional behavior of ${\mathcal S\/}$ in an impact of the system. Such a model restores determinism and avoids the analysis of frictional forces in the contact point, with all its associated theoretical problems of causality. Three examples of increasing complexity, showing a natural stick--slip behavior of the impact, are presented.

math-ph↗

arXiv2019

An algorithmic approach to the multiple impact of a disk in a corner

We present the algorithmic procedure determining the impulsive behavior of a rigid disk having a single or possibly multiple frictionless impact with two walls forming a corner. The algorithmic procedure represents an application of the general theory of multiple impacts as presented in \cite{Pasquero2016Multiple} for the ideal case. In the first part, two theoretical algorithms are presented for the cases of ideal impact and Newtonian frictionless impact with global dissipation index. The termination analysis of the algorithms differentiates the two cases: in the ideal case, we show that the algorithm always terminates and the disk exits from the corner after a finite number of steps independently of the initial impact velocity of the disk and the angle formed by the walls; in the non--ideal case, although is not proved that the disk exits from the corner in a finite number of steps, we show that its velocity decreases to zero and the termination of the algorithm can be fixed through an "almost at rest" condition. In the second part, we present a numerical version of both the theoretical algorithms that is more robust than the theoretical ones with respect to noisy initial data and floating point arithmetic computation. Moreover, we list and analyze the outputs of the numerical algorithm in several cases.

math.NA↗

arXiv2018

A survey about framing the bases of Impulsive Mechanics of constrained systems into a jet-bundle geometric context

We illustrate how the different kinds of constraints acting on an impulsive mechanical system can be clearly described in the geometric setup given by the configuration space--time bundle $π_t:\mathcal{M} \to \mathbb{E}$ and its first jet extension $π: J_1 \to \mathcal{M}$ in a way that ensures total compliance with axioms and invariance requirements of Classical Mechanics. We specify the differences between geometric and constitutive characterizations of a constraint. We point out the relevance of the role played by the concept of frame of reference, underlining when the frame independence is mandatorily required and when a choice of a frame is an inescapable need. The thorough rationalization allows the introduction of unusual but meaningful kinds of constraints, such as unilateral kinetic constraints or breakable constraints, and of new theoretical aspects, such as the possible dependence of the impulsive reaction by the active forces acting on the system.

math-ph↗

arXiv2011

Conditions for the feasibility of multiple rolling for mechanical systems with multiple contact points

We illustrate a theoretical procedure determining necessary conditions for which simultaneous pure rolling kinetic constraints acting on a mechanical system can be fulfilled. We also analyze the sufficiency of these conditions by generalizing to this case a well known and usually accepted assumption on the behavior of pure rolling constraint. We present in detail the application of the procedure to some significative mechanical systems.

physics.class-ph↗

arXiv2007

Some results on ideal impacts of billiard balls

We analyze the impact of two equal billiard balls in three ideal situations: when the balls freely slide on the plane of the billiard, when they roll without sliding and when one of them freely slides and the other rolls. In all the cases we suppose that the contact between the balls is smooth. We base our analysis on some recent general theoretical results on ideal impacts obtained by means of Differential Geometric Impulsive Mechanics. We use symbolic computation software to solve the computational difficulties arising by the high number of degrees of freedom of the system. Some particular but significative impacts, with opportunely assigned left velocities and positions of the balls, are analyzed in details. The results admit easy interpretations that turn out to be in good agreement with the reasonable forecasts and the behaviours of real systems.

physics.class-ph↗