The Paradoxical Asymptotic Status of Massless Springs

DOI10.1137/0148081zbMath0661.73018OpenAlexW2043139466MaRDI QIDQ3811813

Stuart S. Antman

Publication date: 1988

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/1903/4619

zbMATH Keywords

asymptoticsordinary differential equationlimiting caseelastic springsmotion of a material pointfunctional differential equation with memorymass density goes to zerospring with massviscoelastic springs

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Vibrations in dynamical problems in solid mechanics (74H45) Thin bodies, structures (74K99) Dynamics of a system of particles, including celestial mechanics (70F99) Nonlinear dynamics in mechanics (70K99) Nonlinear constitutive equations for materials with memory (74D10) General theory of functional equations and inequalities (39B05)

Related Items (7)

Asymptotics and attractors for quasilinear parabolic-hyperbolic systems governing the motions of heavily burdened deformable bodies ⋮ Global attractors for quasilinear parabolic-hyperbolic equations governing longitudinal motions of nonlinearly viscoelastic rods ⋮ The asymptotic problem for the springlike motion of a heavy piston in a viscous gas ⋮ The asymptotics of heavily burdened viscoelastic rods ⋮ Dynamical problems for geometrically exact theories of nonlinearly viscoelastic rods ⋮ The motion of a particle on a light viscoelastic bar: asymptotic analysis of its quasilinear parabolic-hyperbolic equation. ⋮ Invariant manifolds describing the dynamics of a hyperbolic–parabolic equation from nonlinear viscoelasticity

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