Periodic motion of a mass–spring system

The equations of planar motion of a mass attached to two anchored massless springs form a symmetric Hamiltonian system. The system has a single dimensionless parameter L, corresponding to the spacing between the anchors. For L > 1, there is a stable equilibrium at which the springs are in tension...

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Published in:IMA journal of applied mathematics 2009-12, Vol.74 (6), p.807-826
Main Authors: Shearer, Michael, Gremaud, Pierre, Kleiner, Kristoph
Format: Article
Language:English
Subjects:
Exact sciences and technology
Global analysis, analysis on manifolds
Hamiltonian system
mass-spring system
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Operator theory
periodic solutions
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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creator Shearer, Michael
Gremaud, Pierre
Kleiner, Kristoph
description The equations of planar motion of a mass attached to two anchored massless springs form a symmetric Hamiltonian system. The system has a single dimensionless parameter L, corresponding to the spacing between the anchors. For L > 1, there is a stable equilibrium at which the springs are in tension and lie on a line, but for L 
doi_str_mv 10.1093/imamat/hxp032
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The system has a single dimensionless parameter L, corresponding to the spacing between the anchors. For L &gt; 1, there is a stable equilibrium at which the springs are in tension and lie on a line, but for L &lt; 1, this equilibrium has both springs in compression and is unstable. However, there are then two stable equilibria at which both springs carry no force. 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subjects Exact sciences and technology
Global analysis, analysis on manifolds
Hamiltonian system
mass-spring system
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Operator theory
periodic solutions
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
title Periodic motion of a mass–spring system
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