Wyniki wyszukiwania - Biblioteka Nauki

1

Dynamics of a backlash chain

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Machado J.

Open Physics

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2013

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tom 11

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nr 10

1268-1274

EN

This paper studies the dynamical properties of a system with distributed backlash and impact phenomena. This means that it is considered a chain of masses that interact with each other solely by means of backlash and impact phenomena. It is observed the emergence of non-linear phenomena resembling those encountered in the Fermi-Pasta-Ulam problem.

2

Chaotic vibration of an autoparametrical system with a non-ideal source of power

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Sado D. , Kot M.

Journal of Theoretical and Applied Mechanics

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2007

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tom Vol. 45 nr 1

119-131

EN

This paper studies the dynamical coupling between energy sources and the response of a two degrees of freedom autoparametrical system, when the excitation comes from an electric motor (with unbalanced mass mo), which works with limited power supply. The investigated system consists of a pendulum of the length l and mass m, and a body of mass M suspended on a flexible element. In this case, the excitation has to be expressed by an equation describing how the energy source supplies the energy to the system. The non- ideal source of power adds one degree of freedom, which makes the system have three degrees of freedom. The system has been searched for known characteristics of the energy source (DC motor). The equations of motion have been solved numerically. The influence of motor speed on the phenomenon of energy transfer has been studied. Near the internal and external resonance region, except for different kinds of periodic vibration, chaotic vibration has been observed. For characterizing an irregular chaotic response, bifurcation diagrams and time histories, power spectral densities, Poincare maps and maximaI exponents of Lyapunov have been developed.

PL

W pracy uwzględniono wzajemne oddziaływania autoparametrycznego układu drgającego o dwóch stopniach swobody i układu wymuszającego, którym jest silnik elektryczny z niewyważoną masą o znanej charakterystyce. Układ podstawowy składa się z wahadła o długości l i masie m podwieszonego do ciała o masie M zawieszcnego na elemencie sprężystym. Uwzględniając nieidealne źródło energii dodaje się do badanego układu dodatkowy stopień swobody, bada się więc układ o trzech stopniach swobody, ale czas nie występuje w równaniach w postaci jawnej. Równania ruchu rozwiązywano numerycznie i badano drgania w pobliżu rezonansu wewnętrznego i rezonansu zewnętrznego. W tym zakresie parametrów oprócz różnego rodzaju drgań regularnych mogą wystąpić również drgania chaotyczne. Charakter drgań nieregularnych weryfikowano analizując diagramy bifurkacyjne, przebiegi czasowe, transformaty Fouriera, mapy Poincare oraz maksymalne wykładniki Lapunowa.

3

Modelling and simulation of dynamic unilateral elasto-plastic contact of compact hard bodies

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Kowalska Z.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2002

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tom Vol. 6, No 3

335-341

EN

The problems of modelling, simulation and analysis of vibro-impact motion of compact hard bodies are considered. In particular, dynamic elasto-plastic contact is simulated by using Johnson's analytical model of spherical bodies' contact. The results are compared with behaviour of the system with discrete linear-perfectly plastic model of contact.

4

The Nosé-Hoover, Dettmann, and Hoover-Holian Oscillators

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Hoover W. G. , Sprott J. C. , Hoover C. G.

Computational Methods in Science and Technology

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2019

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tom Vol. 25, No. 3

121--124

EN

To follow up recent work of Xiao-Song Yang [1] on the Nosé-Hoover oscillator [2–5] we consider Dettmann’s harmonic oscillator [6, 7], which relates Yang’s ideas directly to Hamiltonian mechanics. We also use the Hoover-Holian oscillator [8] to relate our mechanical studies to Gibbs’ statistical mechanics. All three oscillators are described by a coordinate q and a momentum p. Additional control variables (ζ, ξ) vary the energy. Dettmann’s description includes a time-scaling variable s, as does Nosé’s original work [2, 3]. Time scaling controls the rates at which the (q, p, ζ) variables change. The ergodic Hoover-Holian oscillator provides the stationary Gibbsian probability density for the time-scaling variable s. Yang considered qualitative features of Nosé-Hoover dynamics. He showed that longtime Nosé-Hoover trajectories change energy, repeatedly crossing the ζ = 0 plane. We use moments of the motion equations to give two new, different, and brief proofs of Yang’s long-time limiting result.

5

Filtering Poincaré plots

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Piskorski J. , Guzik P.

Computational Methods in Science and Technology

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2005

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tom Vol. 11, nr 1

39-48

EN

The Poincaré plot (PP) is one of the many techniques used for ascertaining the heart rate variability, which in turn is a marker of the activity of the autonomic system. Poincaré plots are very simple to produce, but their preparation involves a few fine points. This paper describes one of them, namely the filtering of data used for the Poincaré plot. We show the correct way of filtering data, present a few results of not filtering or incorrect filtering and demonstrate how proper filtering helps extract interesting information from the data. A few algorithms for preparing Poincaré plots, filtering data and calculating PP descriptors are included. As Matlab’s programming language is the unquestionable standard for data analysis in the medical sciences, we illustrate these algorithms by snippets of code in this language.

6

Application of the Energy Space in Chaotic Systems Research

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Dąbrowski A.

Mechanics and Mechanical Engineering

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2007

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tom Vol. 11, nr 1

21-35

EN

The new method of dynamic systems control is presented. Energy-vector space is introduced. Transformations of the traditional phase space to obtain the energy space. Applications of the new type system research are shown. Different types of systems dynamics are analysed with use of the energy space. Stability of the system is analysed with use of the Stefaski method of the largest Lyapunov exponent calculation [12]. New kind of maps are introduced and applied to examine system dynamics.

7

On tuning mechanisms of DPF devices

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Tsybenko S. , Miklaszewski R.

Nukleonika

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2000

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tom Vol. 45, nr 3

163-165

EN

A global instability theory of pinching plasmas allows us to justify the well-known empirical facts of the use of a mismatched dense plasma focus (DPF) and heavy inert gas admixtures. We assume that an instability of tangential discontinuity is responsible for the instability of a current-carrying plasma column. To inhibit development of a tangential discontinuity in a plasma focus, an array of insulator fibers or metallic wires placed on the anode near the axis of a discharge camera can be used.

8

Weakly nonlinear dynamics of short acoustic waves in exponentially stratified gas

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Perelomova A.

Archives of Acoustics

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2009

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tom Vol. 34, No. 2

197-213

EN

The types of linear motion over an ideal gas affected by gravity are specified approximately in the case of large characteristic wave number of perturbation k: k>> 1/H, where H is the scale of density and pressure decrease of the background gas, the so-called height of the uniform gas. The corresponding approximate operators projecting the overall vector of perturbations into specific types are derived, along with equations governing sound in a weakly nonlinear flow. The validity of approximate formulae are verified for the concrete examples of initial waveforms. The numerical analysis reveals a good agreement of these approximate expressions with the exact ones obtained previously by the author. The analysis applies to the weakly nonlinear flow as well, with the small Mach numbers (M<<1). The links inside modes are redetermined by including terms of order M2 and M2/kH.

9

Chaotic dynamics in iterated map neutral networks with piecewise linear activation function

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Sinha S.

Fundamenta Informaticae

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1999

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tom Vol. 37, Nr 1,2

31-50

EN

The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibi-tory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair neurons (one excitatory and the other inhibitory) connected with each other, is studied in detail. Even such a simple system shows a rich variety of behavior, includ-ing high-period oscillations and chaos. Border-collision bifurcations and multifractal fragmentation of the phase space is also observed for a range of parameter values. Extension of the model to a larger number of neurons is suggested under certain restrictive assumptions, which makes the resultant network dynamics effectively one-dimensional. Possible applica-tions of the network for information processing are outlined. These include using the network for auto-association, pattern classification, nonlinear function approximation and periodic sequence generation.

10

Modified semi-analytical approach for duffing equation

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Amara U. E. , Rehman S. , Abbas M. , Rehman J. U.

Acta Mechanica et Automatica

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2024

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tom Vol. 18, no. 2

300--306

EN

This research endeavour-investigates the enhanced adaptation of the Laplace-based variational iteration method (VIM) tailored specifically for tackling the Duffing Equation. This is accomplished by incorporating the Lagrange multiplier as a strategic tool to effectively address the inherent natural frequency within the Duffing Equation. Using a meticulous comparative analysis, here are juxtapose the ana-lytical outcomes generated by the modified VIM approach with the numerical solution obtained through the application of the renowned Runge-Kutta Fehlberg method (RKF45), implemented by using the powerful mathematical software, MAPLE. Furthermore, by exploring the

11

Investigation of the pad stiffness effects on the initiation of brake squeal phenomenon

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Yavuz A. , Sen O.

Journal of Theoretical and Applied Mechanics

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2023

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tom Vol. 61 nr 2

219--232

EN

The main objective of this study is to investigate pad stiffness effects on the instability of a nonlinear brake squeal model. Hence, a nonlinear mathematical model is developed. The nonlinear model is linearized to check the system stability through complex eigenvalue analysis. The results of linear stability analyses are compared to the numerical solution of the nonlinear model, and it is observed that the dynamic behavior predicted by the linear stability analysis is in accordance with the numerical solutions. Though, a discrepancy may occur at the predicted squeal frequencies with both approaches, especially at high pad stiffness levels.

12

Extension of the Hamiltonian approach with general initial conditions

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Navarro H. A. , Cveticanin L.

Journal of Theoretical and Applied Mechanics

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2018

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tom Vol. 56 nr 1

255--267

EN

In this paper, the Hamiltonian approach is extended for solving vibrations of nonlinear conservative oscillators with general initial conditions. Based on the assumption that the derivative of Hamiltonian is zero, the frequency as a function of the amplitude of vibration and initial velocity is determined. A method for error estimation is developed and the accuracy of the approximate solution is treated. The procedure is based on the ratio between the average residual function and the total energy of the system. Two computational algorithms are described for determining the frequency and the average relative error. The extended Hamiltonian approach presented in this paper is applied for two types of examples: Duffing equation and a pure nonlinear conservative oscillator.

13

Linear genetic programming control for strongly nonlinear dynamics with frequency crosstalk

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Li R. , Noack B. , Cordier L. , Borée J. , Kaiser E. , Harambat F.

Archives of Mechanics

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2018

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tom Vol. 70, nr 6

505--534

EN

We advance Genetic Programming Control (GPC) for turbulence flow control application building on the pioneering work of [1]. GPC is a recently proposed model-free control framework which explores and exploits strongly nonlinear dynamics in an unsupervised manner. The assumed plant has multiple actuators and sensors and its performance is measured by a cost function. The control problem is to find a control logic which optimizes the given cost function. The corresponding regression problem for the control law is solved by employing linear genetic programming as an easy and simple regression solver in a high-dimensional control search space. This search space comprises open-loop actuation, sensor-based feedback and combinations thereof — thus generalizing former GPC studies [2, 3]. This new methodology is denoted as linear genetic programming control (LGPC). The focus of this study is the frequency crosstalk between unforced, unstable oscillation and the actuation at different frequencies. LGPC is first applied to the stabilization of a forced nonlinearly coupled three-oscillator model comprising open- and closed-loop frequency crosstalk mechanisms. LGPC performance is then demonstrated in a turbulence control experiment, achieving 22% drag reduction for a simplified car model. In both cases, LGPC identifies the best nonlinear control achieving the optimal performance by exploiting frequency crosstalk. Our control strategy is suited to complex control problems with multiple actuators and sensors featuring nonlinear actuation dynamics. Significant further performance enhancement is envisioned in the more general field of machine learning control [4].

14

Dynamical jump attenuation in a non-ideal system through a magnetorheological damper

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Piccirillo V. , Tusset A. M. , Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2014

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tom Vol. 52 nr 3

595--604

EN

This paper is concerned with the Sommerfeld effect (Jump phenomena) attenuation in an non-ideal mechanical oscillator connected with an unbalanced motor excitation with a limited power supply (non-ideal system) using a magnetorheological damper (MRD). The dynamical response of systems with MRD presents different behavior due to their nonlinear characteristic. MRD nonlinear response is associated with adaptive dissipation related to their hysteretic behavior. The Bouc-Wen mathematical model is used to represent the MRD behavior. Numerical simulations show different aspects about the Sommerfeld effect, illustrating the influence of the different electric current applied in the MRD to control the force developed by this damper.

15

Light polarization fingerprints on nonlinear dynamics of vertical-cavity surface-emitting lasers

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Panajotov K. , Sciamanna M. , Gatare I. , Arizaleta Arteaga M. , Thienpont H.

Opto-Electronics Review

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2008

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tom Vol. 16, No. 4

337-346

EN

In this paper we summarize the recent results on nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) which are bearing the fingerprints of the particular polarization properties of VCSELs. Due to the surface emission and cylindrical symmetry, VCSELs lack strong polarization anisotropy and may undergo polarization switching and polarization mode-hopping. This provides new specificities to the rich nonlinear dynamics induced in VCSELs by an external perturbation. We unveil both experimentally and theoretically these new specificities for the case of optical feedback, optical injection, and unidirectional synchronization between VCSELs.

16

Thinking Through Tools: What Can Tool-Use Tell Us About Distributed Cognition?

100%

Baber C.

Studies in Logic, Grammar and Rhetoric

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2015

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tom 41

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nr 1

25-40

EN

In this paper, I question the notion that tool-use must be driven by an internal representation which specifies the “motor program” enacted in the behaviour of the tool-user. Rather, it makes more sense to define tool-use in terms of characteristics of the dynamics of this behaviour. As the behaviour needs to be adjusted to suit changes in context, so there is unlikely to be a one-to-one, linear mapping between an action and its effect. Thus, tool-use can best be described using concepts from Nonlinear Dynamics. Such an approach can be used to create a sort of cybernetic model of tool-use. However, there is a danger that such a model can either lead us back to internal representations (in that the comparator used to evaluate feedback during behaviour could be assumed to be pre-defined) or could fail to capture cognitive aspects of behaviour. In particular, the question of how the craftworker’s intent can be enacted in the use of tools to produce a specific object seems to be lost in the cybernetic account. My solution is two-fold. First, the “model” is created on-the-fly and adapted through moment-by-moment interactions in the system of tool-user–tool–material–environment. This means that, rather than assuming a pre-defined internal representation that drives behaviour, I propose that cognition involves the selection of salient parameters that characterize the behaviour and the continued monitoring and management of behaviour in terms of these parameters. Second, intent is only loosely defined a priori but crystallizes through the continued interactions between craftworker and object through a process in which the affordances of the object become apparent to, and responded to by, the craftworker.

17

Rocking of freestanding objects: theoretical and experimental comparisons

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Gesualdo A. , Iannuzzo A. , Minutolo V. , Monaco M.

Journal of Theoretical and Applied Mechanics

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2018

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tom Vol. 56 nr 4

977--991

EN

The methodical study of safeguard of artistic heritage and other devices subjected to earthquake and, in general, to time-dependent forces has considerably spreaded in the last years, thus increasing researchers’ interest in problems concerning motions of rigid objects simply supported on a base plane. The behaviour of piece of equipments, statues, storage tanks, or even tall buildings has been in fact studied as that of rigid bodies with relation to different base excitations. In some cases, the possibility of influencing the quality of motion can be a strong tool to reduce vulnerability, like in the cases in which rocking motion is to be avoided and sliding motion is welcome. This paper focuses the attention on this last problem. This is the same large class of both non-structural and structural elements that can lose their functionality because of earthquake motions. The results of numerical modelling of sliding and rocking motion in presence of both different excitations and mechanical parameters are presented and compared with experimental data performed by the authors. The results developed are in good agreement with the laboratory tests, and this assures the reliability of both the analytical procedure and the determination of the parameters involved.

18

Nonlinear discrete-continuous models in the analysis of low structures subject to kinematic excitations caused by transversal waves

100%

Pielorz A.

Journal of Theoretical and Applied Mechanics

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1998

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tom nr 4

979-999

EN

The paper deals with dynamic analysis of low structures subject to kinematic excitations caused by transversal waves when using nonlinear discrete-continuous models. The models consist of rigid bodies and elastic elements which undergo only shear deformations. In these models discrete elements with a damper and a spring of a nonlinear characteristic representing local nonlinearities can be included. In the study a wave approach is used, in terms of the wave solution of the equations of motion. Numerical calculations are performed for model with single, two, three or four rigid bodies. They focus on the determination of amplitudefrequency curves and investigation into the effect of local nonlinearities on displacements of selected cross-sections of elastic elements in the considered models.

PL

Praca dotyczy analizy dynamicznej niskich obiektów poddanych poprzecznym wymuszeniom kinematycznym wykorzystując nieliniowe modele dyskretno-ciągłe. Modele te składają się z brył sztywnych i elementów sprężystych poddanych tylko odkształceniom ścinającym. W modelach tych można uwzględnić dyskretne elementy ze sprężyną o nieliniowej charakterystyce reprezentujące lokalne nieliniowości. W rozważaniach zastosowano metodę falową, w której wykorzystuje się rozwiązanie falowe równań ruchu. Obliczenia numeryczne wykonano dla modeli z jedną, dwiema, trzema i czterema bryłami sztywnymi. Koncentrują się one na wyznaczaniu krzywych amplitudowo-częstotliwościowych i badaniu wpływu parametrów reprezentujących lokalną nieliniowość na przemieszczenia w wybranych przekrojach poprzecznych elementów sprężystych rozważanych układów dyskretno-ciągłych.

19

The Yang-Mills fields - from the gauge theory to the mechanical model

100%

Constantinescu R. , Ionescu C.

Open Physics

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2009

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tom 7

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nr 4

711-720

EN

The paper presents some mechanical models of gauge theories, i.e. gauge fields transposed in a space with a finite number of degree of freedom. The main focus is on how a global symmetry as the BRST one could be transferred in this context. The mechanical Yang-Mills model modified by taking the ghost type variables into account will be considered as an example of nonlinear dynamical systems.

20

Application of artificial neural networks in parametrical investigations of the energy flow and synchronization

100%

Dąbrowski A. , Jach A. , Kapitaniak T.

Journal of Theoretical and Applied Mechanics

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2010

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tom Vol. 48 nr 4

871-896

EN

Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.

PL

Dynamika układów nieliniowych jest bardzo komplikowanymzagadnieniem z wieloma aspektami wciąż pozostającymi bez rozwiązania. Do badań takich układów stosuje się wiele różnych metod. Wnikliwa analiza związana jest najczęściej z bardzo czasochłonnymi symulacjami numerycznymi. Istnieje w związku z tym duże zapotrzebowanie na opracowanie metod upraszczających ten proces. W artykule pokazano zastosowanie sztucznych sieci neuronowych (ANN) wspomagających badania przepływu i synchronizacji energii. W badaniach zastosowano Mapy Uderzeń, będące efektem przedstawienia dynamiki układu z uderzeniami w przestrzeni energetyczno-wektorowej. Pokazano zmiany przepływu energii z przejściowym stanem synchronizacji. Wprowadzono nowy rodzaj parametru pozwalającego na określanie stanu dynamicznego układu z uderzeniami. Wyniki przeprowadzonych symulacji numerycznych zostały wykorzystane w procesie uczenia sztucznej sieci neuronowej. Przedstawiono następnie porównanie wyników symulacji i rozwiązania uzyskanego z sieci neuronowej oraz przewidywania parametrów układu, dla których występuje synchronizacja przepływu energii.