On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I: Existence of a wide class of Lagrangian systems capable of motions with bursting characters
type: Item
instance of: scholarly article
title: On motions with bursting characters for Lagrangian mechanical systems with a scalar control. I: Existence of a wide class of Lagrangian systems capable of motions with bursting characters
zbMATH Open document ID: 0784.70025
author: Aldo Bressan
author: Marco Favretti
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 1992-09-27T00:00:00Z
full work available at URL: https://eudml.org/doc/244273
review text: The authors report results of papers of theirs which are concerned with mechanical systems with a scalar control parameter. The so-called semi- Hamiltonian equation \(\dot z=F\bigl[t,u(t),z,\dot u(t)\bigr]\) governs the dynamics of the system, where \(z=(q,p)\) are the generalised coordinates and moments and \(u(t)\) is the control parameter, which can have discontinuities (hyper-impulsive motions). The reported theorems state conditions for \(F\) (with respect to the dependence of \(\dot u(t))\) and the corresponding kinetic energy whether the solutions have (no) bursting character and how the solutions depend on the discontinuities.
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 70H03
Mathematics Subject Classification ID: 93B52
zbMATH DE Number: 61700
zbMATH Keywords: dynamical systems
zbMATH Keywords: hyper-impulsive motions
zbMATH Keywords: control parameter
zbMATH Keywords: semi- Hamiltonian equation
zbMATH Keywords: discontinuities
zbMATH Keywords: kinetic energy
reviewed by: Gerhard Gerlich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 61700