The general problem of the stability of motion

By A. M. Lyapunov. 1994

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Citations in the corpus

A CONSTRUCTIVE CONVERSE LYAPUNOV THEOREM ON EXPONENTIAL STABILITY (2004, methodology): “An English translation of his work can be found in [4] Lyapunov's direct method is a mathematical extension of the fundamental physical observation, that an energy dissipative system must eventually settle down to an equilibrium point.”
Reversible Architectures for Arbitrarily Deep Residual Neural Networks (2017, background): “The question is, what would be the change after some time t, that is, what is δY(t)? This change can be characterized by the Lyapunov exponent (Lyapunov 1992), which measures the difference in the trajectories of a nonlinear dynamical system given the initial conditions.”
On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet (2003, methodology): “Unlike all other reported perturbation and non-perturbation techniques such as the artificial small parameter method (Lyapunov 1892), the δ-expansion method (Karmishin, Zhukov & Kolosov 1990; Awrejcewicz, Andrianov & Manevitch 1998) and Adomian’s (1976, 1994) decomposition method, the homotopy analy”
The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems (2014, unknown): “It was originally defined by Lyapunov[29] and Rosenberg[30], its definition being then extended to the following: a NNM is a (nonnecessarily synchronous) periodic motion of the conservative system.”
Are eikonal quasinormal modes linked to the unstable circular null geodesics (2017, background): “The stability can be analyzed in terms of the so called Lyapunov exponents [15].”
Notes on the homotopy analysis method: Some definitions and theorems (2009, methodology): “Using them, Liao [21] proved that the HAM logically contains other previous non-perturbation methods, such as Lyapunov’s artificial small parameter method [13], the d-expansion method [14,15] and Adomian’s decomposition method [16–19].”
Review on computational methods for Lyapunov functions (2015, background): “In 1892 Lyapunov published his famous doctoral dissertation [158], where he introduced a suﬃcient condition for the stability of a nonlinear system, namely, the existence of a positive deﬁnite function decreasing along the solution trajectories.”
Comparison between the homotopy analysis method and homotopy perturbation method (2005, methodology): “As pointed out by Liao ([2], Chapter 4), the homotopy analysis method logically contains Adomian s decomposition method [14], Lyapunov s artificial small parameter method [15], and the d-expansion method [16].”
Piecewise Linear Control Systems (2003, methodology): “Quadratic stability dates back to the pioneering work of Lyapunov [89, 90], who established that the existence of a quadratic Lyapunov function is a necessary and sufficient condition for asymptotic stability of a linear system.”
Comparison between the HAM and HPM solutions of thin film flows of non-Newtonian fluids on a moving belt (2007, methodology): “Besides, it logically contains other nonperturbation technique such as Lyapunov’s small parameter method [13], the δ-expansion method [14] and”