Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

Vesković, M.; Čović, V.; Obradović, Aleksandar

doi:10.1007/s10483-011-1407-9

Cited by 3 publications

(3 citation statements)

References 15 publications

(35 reference statements)

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“…In this way, the algebraic criteria occurring in [14,16,[20][21][22][23] are substituted here by the criterion without the variable κ 1 . In this way, the existence of the vector e satisfying A 1 = λe, λ > 0 is proved.…”

Section: Theorem On Instability -Case Amentioning

confidence: 99%

Lyapunov-Kozlov method for singular cases

Čović

Djuric

Vesković

et al. 2011

Appl. Math. Mech.-Engl. Ed.

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Lyapunov's first method, extended by Kozlov to nonlinear mechanical systems, is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces. The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position. This fact renders the impossible application of Lyapunov's approach in the analysis of the stability because, in the equilibrium position, the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled. It is shown that Kozlov's generalization of Lyapunov's first method can also be applied in the mentioned cases on the conditions that, besides the known algebraic expression, more are fulfilled. Three theorems on the instability of the equilibrium position are formulated. The results are illustrated by an example.

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Section: Theorem On Instability -Case Amentioning

confidence: 99%

Lyapunov-Kozlov method for singular cases

Čović

Djuric

Vesković

et al. 2011

Appl. Math. Mech.-Engl. Ed.

Self Cite

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“…Literature related to the issue of explicit analysis of analytical mechanics and system motion, controllability and stability can be found in [2][3][4][5][6][7]. A significant overview of papers related to 𝑛-dimensional rigid body dynamics is provided in [8] while the papers in the field of the system stability problems can also be found in [9] and [10]. This article suggests a different approaches for the modelling predefined multibody system with the theoretically-based review.…”

Section: Introductionmentioning

confidence: 99%

Modelling and stability analysis of the nonlinear system

Vesović

Radulović

2022

Theor appl mech (Belgr)

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The production industries have repeatedly combated the problem of system modelling. Successful control of a system depends mainly on the exactness of the mathematical model that predicts its dynamic. Different types of studies are very common in the complicated challenges involving the estimations and approximations in describing nonlinear machines are based on a variety of studies. This article examines the behaviour and stability of holonomic mechanical system in the arbitrary parameter sets and functional configuration of forces. Differential equations of the behaviour are obtained for the proposed system on the ground of general mechanical theorems, kinetic and potential energies of the system. Lagrange?s equations of the first and second kind are introduced, as well as the representation of the system in the generalized coordinates and in Hamilton?s equations. In addition to the numerical calculations applied the system, the theoretical structures and clarifications on which all of the methods rely on are also presented. Furthermore, static equilibriums are found via two different approaches: graphical and numerical. Above all, stability of motion of undisturbed system and, later, the system that works under the action of an external disturbance was inspected. Finally, the stability of motion is reviewed through Lagrange-Dirichlet theorem, and Routh and Hurwitz criteria. Linearized equations are obtained from the nonlinear ones, and previous conclusions for the stability were proved.

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“…Moreover, stability of the specific mechanical system was discussed using different approaches. Namely, unlike the papers [8] and [9], where the relative advantages and disadvantages of various analytical methods of nonholonomic systems are briefly presented, the problem of the instability of the equilibrium state of a scleronomic mechanical system with linear homogeneous constraints are considered in [10], and the problem of the stability of the equilibrium state in the case with holonomic mechanical systems in [11].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

Vesović¹,

Petrović²,

Radulović³

2021

FME Transactions

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In order to give an insight into the work of the machine before the production and assembly and to obtain good analysis, this paper presents detailed solutions to the specific problem occured in the field of analytical mechanics. In addition to numerical procedures in the paper, a review of the theoretical foundations was made.Various types of analysis are very common in mechanical engineering, due to the possibility of an approximation of complex machines. For the proposed system, Lagrange's equations of the first kind, covariant and contravariant equations, Hamiltons equations and the generalized coordinates, as well as insight in Coulumb friction force are provided.Also, the conditions of static equilibrium are solved numerically and using intersection of the two curves. Finally, stability of motion for the disturbed and undisturbed system was investigated.

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Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

Cited by 3 publications

References 15 publications

Lyapunov-Kozlov method for singular cases

Lyapunov-Kozlov method for singular cases

Modelling and stability analysis of the nonlinear system

Analysis of the motion and stability of the holonomic mechanical system in the arbitrary force field

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