共查询到20条相似文献,搜索用时 31 毫秒
1.
Stuart S. Antman 《Journal of Nonlinear Science》2011,21(4):595-638
This paper treats the rich mathematical structure of the (dimensionless) equation of motion governing the behavior of an elastically
restrained simple pendulum subject to a downward force of magnitude f(t) applied to its bob with $\dot{f}(t)>0$\dot{f}(t)>0 for all t>0 and f(t)→∞ as t→∞:
[(q)\ddot]+2n[(q)\dot] +q = f(t)sinq.\ddot{\theta}+2\nu\dot{\theta} +\theta= f(t)\sin\theta. 相似文献
2.
We study the family of divergence-type second-order parabolic equations
we(x)\frac?u?t=div(a(x)we(x) ?u), x ? \mathbbRn{\omega_\varepsilon(x)\frac{\partial u}{\partial t}={\rm div}(a(x)\omega_\varepsilon(x) \nabla u), x \in \mathbb{R}^n} , with parameter ${\varepsilon >0 }${\varepsilon >0 } , where a(x) is uniformly elliptic matrix and we=1{\omega_\varepsilon=1} for x
n
< 0 and we=e{\omega_\varepsilon=\varepsilon} for x
n
> 0. We show that the fundamental solution obeys the Gaussian upper bound uniformly with respect to e{\varepsilon} . 相似文献
3.
In this paper, we study the planar Hamiltonian system = J (A(θ)x + ▽f(x, θ)), θ = ω, x ∈ R2 , θ∈ Td , where f is real analytic in x and θ, A(θ) is a 2 × 2 real analytic symmetric matrix, J = (1-1 ) and ω is a Diophantine vector. Under the assumption that the unperturbed system = JA(θ)x, θ = ω is reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system. 相似文献
4.
Márcio José Horta Dantas José Manoel Balthazar 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,28(1):940-958
In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E.
[(x)\dot] = f (x) + eg (x, t) + e2[^(g)] (x, t, e){\dot{x} = f (x) + \varepsilon g (x, t) + \varepsilon^{2}\widehat{g} (x, t, \varepsilon)}
, where
x ? W ì \mathbbRn{x \in \Omega \subset \mathbb{R}^n}
,
g,[^(g)]{g,\widehat{g}}
are T periodic functions of t and there is a
0 ∈ Ω such that f ( a
0) = 0 and f ′( a
0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x
3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system:
the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld
Effect as a bifurcation of periodic orbits. 相似文献
5.
In this paper we discuss the existence of positive T-periodic solutions for the following second order differential equation
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