Asymptotical stability of the motion of mechanical systems with partial energy dissipation

Puzyrov, Volodymyr; Awrejcewicz, Jan

doi:10.1007/s11071-017-3872-8

Cited by 4 publications

(3 citation statements)

References 31 publications

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“…In order to make sure that the stabilization procedure is reliable, i.e. solution (23) is asymptotically stable, we have to consider the following matrix [20]…”

Section: F I G U R E 7 Rigid Body With Dashpotmentioning

confidence: 99%

“…At the same time, concerning Theorem 1, as noted in a number of works (see, for instance [14][15][16][17][18][19][20]), the requirement that the matrix characterizing dissipative forces should be positive is in some cases superfluous. In particular, a semi-positive definite matrix as a rule (with the exception of a set of measure zero) makes the stable equilibrium position of the conservative system asymptotically stable.…”

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confidence: 99%

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Pervasive damping in mechanical systems and the role of gyroscopic forces

2019

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In this paper, we analyze the stability problem for autonomous non-conservative mechanical systems in the presence of potential, gyroscopic, and dissipative forces.It is assumed that the dissipation is pervasive, i.e. the matrix of dissipative forces is semi-positive definite. With this requirement, the celebrated Kelvin-Chetaev theorems cannot be applied. Considering this circumstance, we discuss the role of gyroscopic forces and their contribution to the overall phenomenon. This influence may be both positive and negative (there are some sets in space of parameters, where the asymptotic stability of the motion is broken). Moreover, the gyroscopic stabilization, which is neglected by complete dissipative force, may be saved with pervasive damping. We use a special procedure to prove the asymptotical (or marginal) stability. This procedure applied to considered case study is simpler than common algorithms based on the eigenvalues analysis (Routh-Hurwitz or Lienard-Chipart criteria, etc.). We apply this approach for a stability problem of two mechanical systems. The first of them is the problem of a passive stabilization of permanent rotations of Lagrange gyroscope. It is proved that adding a dashpot to a gyroscope with flattened inertia ellipsoid stabilizes permanent rotations of the gyro with the exception of some "critical" values. The last may be found analytically from special conditions. The second one is a rotary oscillating system with the external harmonic excitation. The absorber attached to the rotating frame stabilizes the periodic oscillations of the system. Also we have found the critical (resonant) value, which may be avoided by appropriate choice of the absorber's mass.

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“…In order to make sure that the stabilization procedure is reliable, i.e. solution (23) is asymptotically stable, we have to consider the following matrix [20]…”

Section: F I G U R E 7 Rigid Body With Dashpotmentioning

confidence: 99%

mentioning

confidence: 99%

Pervasive damping in mechanical systems and the role of gyroscopic forces

2019

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“…However, they are a valuable complement to the topic of rigid body motion, which includes the load motion. The motion of rigid bodies as a motion of the mathematical and physical pendulum is shown in works [21][22][23][24][25][26][27]. The deformability of the rope system was included in the paper [21].…”

Section: Introductionmentioning

confidence: 99%

The dynamic analysis of load motion during the interaction of wind pressure

2020

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This work presents the analysis of the load motion during the interaction of wind pressure. The load was treated as a rigid body, and the rope system model as a non-deformed. The influence of effective area of wind pressure on load motion was considered. The theoretical model of load motion was presented, which may be an universal approach for transporting machines equipped with a rope-lifting system. To define the orientation of the movable Cartesian coordinate system related to the load, Bryant angles were used. An algorithm and computational program were developed to allow for analysis of dynamic phenomena. The initial problem was solved with the use of the ode45 calculation procedure in the Matlab software on the basis of the Runge-Kutta 4th Order Method. The obtained results were verified with the experimental ones achieved in the wind tunnel and Tracker program. Numerical calculations using commercial software SolidWorks were also presented. In the experiment, the spatial motion of the load was analysed. Experimental tests were carried out for gust of wind and constant temperature and humidity. In addition, the paper presents the application of the proposed method for a load carried by a rotary crane. After taking into account the control functions resulting from the nature of the work of any machine, the formulated model can be a full description of the carried load motion taking into account external forces.

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A double pendulum fixed at the L1 libration point: a precursor to a Mars–Phobos space elevator

Aslanov

2023

Nonlinear Dyn

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Asymptotical stability of the motion of mechanical systems with partial energy dissipation

Cited by 4 publications

References 31 publications

Pervasive damping in mechanical systems and the role of gyroscopic forces

Pervasive damping in mechanical systems and the role of gyroscopic forces

The dynamic analysis of load motion during the interaction of wind pressure

A double pendulum fixed at the L1 libration point: a precursor to a Mars–Phobos space elevator

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