On the instability of an equilibrium point of a linear oscillator with variable parameters

Ignatyev, Alexander O.

doi:10.1016/0021-8928(91)90025-p

Cited by 10 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, those results can be found in [4][5][6][7][8][9][10] and the references cited therein. It is well known that if both a(t) and b(t) are periodic functions (or constants), then the equilibrium x = x = 0 of (E) is asymptotically stable if and only if it is uniformly asymptotically stable.…”

Section: Introductionmentioning

confidence: 78%

Non-uniform asymptotic stability for the damped linear oscillator

Onitsuka¹

2010

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

Section: Introductionmentioning

confidence: 78%

Non-uniform asymptotic stability for the damped linear oscillator

Onitsuka¹

2010

Nonlinear Analysis: Theory, Methods & Applications

View full text Add to dashboard Cite

“…The asymptotic stability for the classical equation (1.1) has been widely studied in [1,2,4,5,7,8,[10][11][12] by using energy functions and Lyapunov stability and instability theorems. In this paper we use different approach based on integral representations of solutions via different asymptotic solutions (for example WKB solutions) and error estimates technique developed in [3,9,6].…”

Section: Resultsmentioning

confidence: 99%

Asymptotic stability and asymptotic solutions of second-order differential equations

Hovhannisyan

2007

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1-20]. To prove asymptotic stability of secondorder differential equations, we establish stability estimates using integral representations of solutions via asymptotic solutions and error estimates. Several examples are discussed. Main resultsConsider the second-order differential equationwhere the coefficients 2f (t) and g(t, x(t), x (t)) are complex-valued continuous functions of time t.

show abstract

“…In the papers of Cveticanin [5][6][7], the influence of the reactive force on motion has been discussed. Based on the dynamics of the particle with variable mass, the stability conditions of motion and an equilibrium position have been obtained [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Dynamic properties of a body with discontinual mass variation

Cvetićanin

Djukić

2007

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper the procedure for the dynamic analysis of body separation is introduced. Based on the general laws of classical dynamics, the method for obtaining the velocity and the angular velocity of the remainder body during separation is developed. Due to the discontinual mass variation, the jump-like change of the velocity and the angular velocity of the body is evident. Various types of motion of the separated body are considered. Depending on the type of motion of the separated body the dynamic properties of the remainder body are obtained. As a special case the in-plane motion of the body before and after separation is considered. The theoretical considerations are applied for the separation analysis of a rotor (a shaft-disc system). The transient motion of the body after separation is investigated. To prove the correctness of the procedure suggested in the paper, the case when the mass and the moment of inertia of the separated body are infinitesimal is analyzed. The obtained differential equations are the same as those previously obtained.

show abstract

On the instability of an equilibrium point of a linear oscillator with variable parameters

Cited by 10 publications

References 0 publications

Non-uniform asymptotic stability for the damped linear oscillator

Non-uniform asymptotic stability for the damped linear oscillator

Asymptotic stability and asymptotic solutions of second-order differential equations

Dynamic properties of a body with discontinual mass variation

Contact Info

Product

Resources

About