On the asymptotic behavior for a damped oscillator under a sublinear friction.

Jesús Ildefonso Díaz; Amable Liñán

Displaying similar documents to “On the asymptotic behavior for a damped oscillator under a sublinear friction.”

The nonlinearly damped oscillator

Juan Luis Vázquez (2003)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the large-time behaviour of the nonlinear oscillator $m x^{''} + f (x^{'}) + k x = 0,$ where $m, k > 0$ and $f$ is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case $f (x^{'}) = A {| x^{'} |}^{α - 1} x^{'}$ with $α$ real, $A > 0$ . We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in finite time.

The mechanics of the stability of a central orbit

Oliver E. Glenn (1933)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Theory of planetary systems

Oliver E. Glenn (1938)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

Forcing relations for homoclinic orbits of the Smale horseshoe map.

Collins, Pieter (2005)

Experimental Mathematics

Similarity:

Retracts, fixed point index and differential equations.

Rafael Ortega (2008)

RACSAM

Similarity:

Some problems in differential equations evolve towards Topology from an analytical origin. Two such problems will be discussed: the existence of solutions asymptotic to the equilibrium and the stability of closed orbits of Hamiltonian systems. The theory of retracts and the fixed point index have become useful tools in the study of these questions.

Alternative transfers to the NEOs 99942 apophis, 1994 WR12, and 2007 UW1 via derived trajectories from periodic orbits of family G.

de Melo, C.F., Macau, E.E.N., Winter, O.C. (2009)

Mathematical Problems in Engineering

Similarity:

On the Asymptotic Distribution of Closed Orbits for a Class of Open Billiards

Julien, Julien (2010)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 37D40. We explain why the lengths of the closed orbits in a certain class of open billiards are asymptotically equidistributed with respect to the number of their reflections.

Unbounded solutions of positively damped Liénard equations

Changming Ding (1996)

Annales Polonici Mathematici

Similarity:

This paper discusses the asymptotic behavior of solutions of the Liénard equation, especially the global behavior of unbounded solutions, and also gives a class of sufficient and necessary conditions for the orbit of a solution to intersect the vertical isocline.