On the motion of a material point on a moving surface
type: Item
instance of: scholarly article
title: On the motion of a material point on a moving surface
zbMATH Open document ID: 0577.70022
DOI: 10.1007/BF02337054
author: J. Terjéki
author: László Hatvani
published in: Meccanica
publication date: 1985-01-01T00:00:00Z
review text: The authors study the following problem: a material point is constrained to move on the surface \(z-\lambda(t)(x^ 2+y^ 2)\) in a constant vertical field of gravity, with the friction force \(-\alpha(\dot x,\dot y,\dot z)=(-\alpha \dot x,-\alpha \dot y,-\alpha \dot z)\), where \(\lambda \in C^ 2({\mathbb{R}}_+,{\mathbb{R}}_+)\) is decreasing and convex, \(\alpha =const>0\). Sufficient conditions on \(\lambda\) and \({\ddot \lambda}\) are given for the stability and instability of equilibrium \(x=y=z=0\).
Mathematics Subject Classification ID: 70K20
zbMATH DE Number: 3924197
zbMATH Keywords: rheonomic constraints
zbMATH Keywords: moving surface
zbMATH Keywords: gravity
zbMATH Keywords: friction force
zbMATH Keywords: instability of equilibrium
MaRDI profile type: Publication
cites work: Stability theory by Liapunov's direct method
cites work: Q3321529
cites work: Q5822220
full work available at URL: https://doi.org/10.1007/bf02337054
OpenAlex ID: W1991889353
description: scientific article; zbMATH DE number 3924197