Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1911.05247

On generalized Coulomb-Amontons' law in the context of rigid body dynamics

Artur Vaganian
View original source ↗Read source document ↗Export metadata ↓

Abstract

A generalization of Coulomb-Amontons' law of dry friction recently proposed by V. V. Kozlov is considered in the context of rigid body dynamics. Universal requirements for dry friction tensor formulated by V. V. Kozlov are complemented by a condition taking into account the contact nature of dry friction and applied to several models. For the famous Painleve problem a generalized Coulomb-Amontons' force without singularities, yet such that the dissipation takes place only at the point of contact, is found. By the example of the motion of a rigid ball on a plane with a single point of contact, it is shown that these principles are consistent with the well-known equations, studied by G.-G. Coriolis. Further, a ball simultaneously touching two perpendicular planes at two points of contact is considered. The corresponding equations of motion are derived and analyzed. An exact particular solution that describes a technique used in practice in billiards is obtained. It is shown that unlike the single contact case, the Lagrange multipliers can depend on friction coefficients. With this in mind, a generalization of the conditions on the tensor of dry friction for the case of an arbitrary number of contacts is proposed.

Explore related subjects

math.DS

Keep this discovery

BibTeXRIS

Artur Vaganian. 2019-11-10. On generalized Coulomb-Amontons' law in the context of rigid body dynamics. https://doi.org/10.1007/s11071-020-05948-1

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗