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  1. Zeitschrift für angewandte Mathematik und Physik
  2. Zeitschrift für angewandte Mathematik und Physik : Volume 65
  3. Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 5, October 2014
  4. Asymptotic stability of a pendulum with quadratic damping
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Zeitschrift für angewandte Mathematik und Physik : Volume 67
Zeitschrift für angewandte Mathematik und Physik : Volume 66
Zeitschrift für angewandte Mathematik und Physik : Volume 65
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 6, December 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 5, October 2014
Spreading speeds and traveling waves for a nonlocal dispersal equation with convolution-type crossing-monostable nonlinearity
Quasilinear parabolic variational inequalities with multi-valued lower-order terms
Asymptotic stability of a pendulum with quadratic damping
Global existence and exponential decay of the solution for a viscoelastic wave equation with a delay
Stability analysis of an interactive system of wave equation and heat equation with memory
Global nonexistence for nonlinear Kirchhoff systems with memory term
Controllability of fractional neutral stochastic functional differential systems
A note on regularity and uniqueness of natural convection with effects of viscous dissipation in 3D open channels
Criteria for trapped modes in a cranked channel with fixed and freely floating bodies
Circularly polarized wave propagation in a class of bodies defined by a new class of implicit constitutive relations
Optimal energy scaling for a shear experiment in single-crystal plasticity with cross-hardening
Asymmetric motion of a transversely isotropic thermoelastic half-space under time-harmonic buried source
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 4, August 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 3, June 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 2, April 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 65, Issue 1, February 2014
Zeitschrift für angewandte Mathematik und Physik : Volume 64
Zeitschrift für angewandte Mathematik und Physik : Volume 63
Zeitschrift für angewandte Mathematik und Physik : Volume 62
Zeitschrift für angewandte Mathematik und Physik : Volume 61
Zeitschrift für angewandte Mathematik und Physik : Volume 60
Zeitschrift für angewandte Mathematik und Physik : Volume 59
Zeitschrift für angewandte Mathematik und Physik : Volume 58
Zeitschrift für angewandte Mathematik und Physik : Volume 57
Zeitschrift für angewandte Mathematik und Physik : Volume 56
Zeitschrift für angewandte Mathematik und Physik : Volume 55
Zeitschrift für angewandte Mathematik und Physik : Volume 54
Zeitschrift für angewandte Mathematik und Physik : Volume 53
Zeitschrift für angewandte Mathematik und Physik : Volume 52
Zeitschrift für angewandte Mathematik und Physik : Volume 51
Zeitschrift für angewandte Mathematik und Physik : Volume 50
Zeitschrift für angewandte Mathematik und Physik : Volume 49
Zeitschrift für angewandte Mathematik und Physik : Volume 48

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Asymptotic stability of a pendulum with quadratic damping

Content Provider SpringerLink
Author Sugie, Jitsuro
Copyright Year 2013
Abstract The equation considered in this paper is $$x'' + h(t)\:x'|x'| + \omega^2\sin x = 0,$$ where h(t) is continuous and nonnegative for $${t \geq 0}$$ and ω is a positive real number. This may be regarded as an equation of motion of an underwater pendulum. The damping force is proportional to the square of the velocity. The primary purpose is to establish necessary and sufficient conditions on the time-varying coefficient h(t) for the origin to be asymptotically stable. The phase plane analysis concerning the positive orbits of an equivalent planar system to the above-mentioned equation is used to obtain the main results. In addition, solutions of the system are compared with a particular solution of the first-order nonlinear differential equation $$u' + h(t)u|u| + 1 = 0.$$ Some examples are also included to illustrate our results. Finally, the present results are extended to be applied to an equation with a nonnegative real-power damping force.
Ending Page 884
Page Count 20
Starting Page 865
File Format PDF
ISSN 00442275
e-ISSN 14209039
Journal Zeitschrift für angewandte Mathematik und Physik
Issue Number 5
Volume Number 65
Language English
Publisher Springer Basel
Publisher Date 2013-08-25
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Phase plane analysis Asymptotic stability Mathematical Methods in Physics Global stability Comparison of solutions Quadratic damping force Damped pendulum Attractors Oscillation theory, zeros, disconjugacy and comparison theory Theoretical and Applied Mechanics Phase plane analysis, limit cycles Stability theory
Content Type Text
Resource Type Article
Subject Applied Mathematics Physics and Astronomy
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