moment stability
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2021 ◽  
Vol 19 (2) ◽  
pp. 209
Author(s):  
Goran Janevski ◽  
Predrag Kozić ◽  
Ratko Pavlović ◽  
Strain Posavljak

In this paper, the Lyapunov exponent and moment Lyapunov exponents of two degrees-of-freedom linear systems subjected to white noise parametric excitation are investigated. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises. The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining both the almost-sure and the moment stability of a stochastic dynamic system. As an example, we study the almost-sure and moment stability of a thin-walled beam subjected to stochastic axial load and stochastically fluctuating end moments.  The validity of the approximate results for moment Lyapunov exponents is checked by numerical Monte Carlo simulation method for this stochastic system.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xianhua Li ◽  
Liang Wu ◽  
Qing Sun ◽  
Tao Song

Tip-over stability analysis is critical for the success of mobile manipulation of the dual arm, especially in the cases that the dual arm or the mobile platform moves rapidly. Due to strong dynamics coupling between the dual arm and mobile platform, online evaluation of dynamic stability of the mobile dual-arm robot still remains challenging. This paper presents an improved tip-over moment stability criterion dealing with the dual arm and mobile platform interaction and proposes an algorithm for calculating the tip-over stability margin of the arm end in the workspace to analyze the dynamic stability of the wheeled mobile dual-arm robot. The simulations on a four-wheeled mobile dual-arm robot validate the correctness and feasibility of the proposed method.


Author(s):  
Jianhai Bao ◽  
Christoph Reisinger ◽  
Panpan Ren ◽  
Wolfgang Stockinger

In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.


2020 ◽  
Vol 18 (2) ◽  
pp. 219
Author(s):  
Ivan R. Pavlović ◽  
Ratko Pavlović ◽  
Goran Janevski ◽  
Nikola Despenić ◽  
Vladimir Pajković

This paper investigates the almost-sure and moment stability of a double nanobeam system under stochastic compressive axial loading. By means of the Lyapunov exponent and the moment Lyapunov exponent method the stochastic stability of the nano system is analyzed for different system parameters under an axial load modeled as a wideband white noise process. The method of regular perturbation is used to determine the explicit asymptotic expressions for these exponents in the presence of small intensity noises.


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