The motion of a continuous medium in a force field with a rooted singularity
type: Item
instance of: scholarly article
title: The motion of a continuous medium in a force field with a rooted singularity
zbMATH Open document ID: 0647.34005
author: A. A. Rojtvarf
published in: Moscow University Mechanics Bulletin
publication date: 1987-01-01T00:00:00Z
review text: The Newton's equation \(\ddot x= G(u,w,t)+ \sqrt{u}H(\sqrt{u},w,t)\), where \(x\in R^ n\), \(\{u=u(x,t)=0\}\) is the temporal front of the (root) singularity of force, \(x=(u,w)\), \(w\in R^{n-1}\) and G, H are analytic functions is considered. The evolution of the field of velocities of some medium of particles, smooth at initial moment, is analyzed. It turns out that the instantenous velocity field has a singularity 3/2 on the front. Namely, by means of a smooth local change of coordinates \(<x,y>\to <q(t,x,v)\), \(p(t,x,v)>\) it can be reduced to the form \(p_ 1=q_ 1^{3/2}\) if \(q_ 1>0\); 0 if \(q_ 1\leq 0\) and \(p_ 2=...=p_ n=0\). The model has an application in the gravity theory of media.
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 58K99
Mathematics Subject Classification ID: 37N99
zbMATH DE Number: 4056058
zbMATH Keywords: Newton's equation
zbMATH Keywords: singularity
zbMATH Keywords: evolution
zbMATH Keywords: instantenous velocity field
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4056058