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Symmetry
Special Issues
Modeling and Simulation of Mechanical Systems and Symmetry
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Modeling and Simulation of Mechanical Systems and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1920

Special Issue Editor

Dr. Ciro Tordela

E-Mail Website
Guest Editor
Department of Industrial Engineering, University of Naples Federico II, Naples, Italy
Interests: Kalman filtering; system modeling; dynamics and control

Special Issue Information

Dear Colleagues,

Symmetry phenomena are detectable in mechanical systems’ dynamic behaviour under specific changes in their initial conditions or parameter variations. The nonlinear nature of a large set of mechanical and mechatronic systems makes their modelling crucial for creating functional simulation platforms for predicting their dynamic behaviour. Dynamic symmetries are discoverable in mechanical systems through approaches such as lumped parameters and multibody modelling. Furthermore, state observers and controllers can be developed by adopting model-based techniques for monitoring and identifying abnormal behaviours of mechanical systems and controlling their motion to obtain the desired ones. Therefore, mechanical system modelling and simulation are a fundamental step in implementing tools for monitoring and control purposes. This Special Issue aims to disseminate research concerning the theory, practice, and application of mechanical system modelling and simulation approaches, expanding the possibility of integrating them into identification, estimation, and control techniques. Papers are welcome on topics including but not limited to the following:

  • Dynamics of multibody systems;
  • Nonlinear mechanical systems showing symmetric dynamic behaviour;
  • Dynamic stability and control of mechanical systems;
  • Model-based monitoring of mechanical systems;
  • Modelling of mechanical systems for formulating state observers.

We look forward to receiving your contributions.

Dr. Ciro Tordela
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • dynamics
  • model-based estimation
  • model-based control
  • vehicle dynamics
  • symmetric dynamic behaviour
  • multibody

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

22 pages, 2780 KB  
Article
A Sigma-Points Kalman Filter Based Estimation for Railway Pantograph Contact Force Monitoring
by Salvatore Strano, Mario Terzo and Ciro Tordela
Symmetry 2026, 18(4), 597; https://doi.org/10.3390/sym18040597 - 31 Mar 2026
Viewed by 325
Abstract
The reliability of current collection is inextricably linked to the contact efficiency between the pantograph and the catenary, which significantly influences their wear state, particularly dependent on contact force. Direct measurement of pantograph–catenary contact force is typically unsuitable for continuous in-service monitoring due [...] Read more.
The reliability of current collection is inextricably linked to the contact efficiency between the pantograph and the catenary, which significantly influences their wear state, particularly dependent on contact force. Direct measurement of pantograph–catenary contact force is typically unsuitable for continuous in-service monitoring due to the necessity for expensive and intrusive instrumented pantographs. As a result, estimation techniques for determining pantograph contact force from observed pantograph dynamics, without the usage of specific force sensors, have gained popularity in recent years. The present work proposes a model-based estimation strategy for monitoring railway pantograph contact force based on a Central Difference Kalman Filter (CDKF). Only the vertical motion of the pantograph head is needed as a measured output to enable the estimation process. The performance of the proposed estimation framework is evaluated by comparing estimated and simulated data for the coupled pantograph–catenary dynamics. The proposed model-based estimator is suitable for monitoring railway pantograph–catenary systems, as demonstrated by the results obtained in different operating conditions. Moreover, the benefits in using the CDKF are highlighted in terms of manageability of nonlinearities rather than the typically adopted Extended Kalman Filter (EKF) for model-based monitoring purposes. Full article
(This article belongs to the Special Issue Modeling and Simulation of Mechanical Systems and Symmetry)
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32 pages, 3856 KB  
Article
Parameter Identification in Nonlinear Vibrating Systems Using Runge–Kutta Integration and Levenberg–Marquardt Regression
by Şefika İpek Lök, Ömer Ekim Genel, Rosario La Regina, Carmine Maria Pappalardo and Domenico Guida
Symmetry 2026, 18(1), 16; https://doi.org/10.3390/sym18010016 - 21 Dec 2025
Viewed by 855
Abstract
Guided by principles of symmetry to achieve a proper balance among model consistency, accuracy, and complexity, this paper proposes a new approach for identifying the unknown parameters of nonlinear one-degree-of-freedom mechanical systems using nonlinear regression methods. To this end, the steps followed in [...] Read more.
Guided by principles of symmetry to achieve a proper balance among model consistency, accuracy, and complexity, this paper proposes a new approach for identifying the unknown parameters of nonlinear one-degree-of-freedom mechanical systems using nonlinear regression methods. To this end, the steps followed in this study can be summarized as follows. Firstly, given a proper set of input time histories and a virtual model with all parameters known, the dynamic response of the mechanical system of interest, used as output data, is evaluated using a numerical integration scheme, such as the classical explicit fixed-step fourth-order Runge–Kutta method. Secondly, the numerical values of the unknown parameters are estimated using the Levenberg–Marquardt nonlinear regression algorithm based on these inputs and outputs. To demonstrate the effectiveness of the proposed approach through numerical experiments, two benchmark problems are considered, namely a mass-spring-damper system and a simple pendulum-damper system. In both mechanical systems, viscous damping is included at the kinematic joints, whereas dry friction between the bodies and the ground is accounted for and modeled using the Coulomb friction force model. While the source of nonlinearity is the frictional interaction alone in the first benchmark problem, the finite rotation of the pendulum introduces geometric nonlinearity, in addition to the frictional interaction, in the second benchmark problem. To ensure symmetry in explaining model behavior and the interpretability of numerical results, the analysis presented in this paper utilizes five different input functions to validate the proposed method, representing the initial phase of ongoing research aimed at applying this identification procedure to more complex mechanical systems, such as multibody and robotic systems. The numerical results from this research demonstrate that the proposed approach effectively identifies the unknown parameters in both benchmark problems, even in the presence of nonlinear, time-varying external input actions. Full article
(This article belongs to the Special Issue Modeling and Simulation of Mechanical Systems and Symmetry)
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