Lyapunov-Kozlov method for singular cases

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

doi:10.1007/s10483-011-1494-6

Cited by 2 publications

(2 citation statements)

References 17 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Kozlov's generalization (see [1][2][3][4]) of the Lyapunov first method [5] for the case of strongly nonlinear systems of differential equations of motion allows solving the problem of instability of equilibrium position of a mechanical system also for the cases when the conditions of existence and uniqueness of solutions of differential equations of motion (see [6,7]) are not satisfied.…”

Section: Introductionmentioning

confidence: 99%

On the instability of equilibrium position of a mechanical system with singular constraints

et al. 2013

Self Cite

View full text Add to dashboard Cite

Key words Lyapunov first method, nonholonomic system, singular constraints, instability of equilibrium.The Lyapunov first method generalized to the case of nonlinear differential equations is applied to the study of the instability of the equilibrium position of a mechanical system, whose motion is constrained by singular nonholonomic constraints. Starting from the results of S. D. Furta (On the instability of equilibrium position of constrained mechanical systems) three theorems on the instability are formulated. The first theorem considers the case of nonholonomic constraints that do not satisfy the condition of weak nonholonomity. The other two theorems are related to the case of weakly nonholonomic systems. In each of the formulated theorems it is shown that the minimum form of Maclaurin series for the potential energy has not a local minimum. Thus, a contribution has been made to the inversion of Lagrange's theorem.

show abstract

Lyapunov-Kozlov method for singular cases

Cited by 2 publications

References 17 publications

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

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

On the instability of equilibrium position of a mechanical system with singular constraints

Contact Info

Product

Resources

About