Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 4th Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 28 February 2027 | Viewed by 883

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Department of Mechanical Engineering, Transilvania University of Brașov, B-dul Eroilor 20, 500036 Brașov, Romania
Interests: dynamic and multibody systems; computational mechanics; machine learning in mechanical engineering; mechanics of composite materials; advanced materials modelling and simulation
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Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, Viale Orabona 4, 70126 Bari, Italy
Interests: bioengineering and cell mechanics; nanosciences and nanotechnology; optical methods; materials science and characterization; structural optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Although making new contributions to the field of mechanics is often considered challenging, the evolution of technology and numerical calculation techniques has led to a reconsideration of these opinions and the development of increasingly sophisticated models that can predict, as accurately as possible, the phenomena that take place in dynamic systems. Therefore, researchers are studying mechanical systems with complicated behavior, observed in experiments and in computer models. The key requirement is that the system involves a nonlinearity. The impetus in mechanics and dynamical systems has come from a wide range of sources: computer simulation, experimental science, mathematics, and modeling. Computer experiments change the way in which we analyze these systems.

Topics of interest include, but are not limited to, the following:

  • modeling mechanical systems;
  • new methods in dynamic systems;
  • behavior simulation of mechanical systems;
  • nonlinear systems;
  • multibody systems with elastic elements;
  • multiple degrees of freedom;
  • mechanical systems;
  • experimental modal analysis;
  • mechanics of materials. 

Prof. Dr. Maria Luminița Scutaru
Dr. Catalin I. Pruncu
Prof. Dr. Luciano Lamberti
Guest Editors

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Keywords

  • dynamic systems
  • modelling of nonlinearities
  • algorithm
  • computer simulation
  • finite elements method

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Published Papers (1 paper)

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Research

30 pages, 14052 KB  
Article
Mathematical Modeling and Dynamic Trajectory Analysis in a Virtual Reality Welding Simulator
by Nuri Furkan Koçak, Ali Saygın, Fuat Türk and Ahmet Mehmet Karadeniz
Mathematics 2026, 14(9), 1506; https://doi.org/10.3390/math14091506 - 29 Apr 2026
Cited by 1 | Viewed by 577
Abstract
This study presents a mathematical and kinematic modeling framework for analyzing trajectory behavior in a virtual reality (VR) welding simulator. Twenty novice participants performed repeated welding trials across three sessions, with torch trajectories recorded at 50 Hz in the task space. The proposed [...] Read more.
This study presents a mathematical and kinematic modeling framework for analyzing trajectory behavior in a virtual reality (VR) welding simulator. Twenty novice participants performed repeated welding trials across three sessions, with torch trajectories recorded at 50 Hz in the task space. The proposed framework combines trial-level performance descriptors with derivative-based dynamic features, including spectral arc length (SPARC), log-normalized jerk (LNJ), and the number of velocity peaks (NVP), to characterize movement smoothness, intermittency, and longitudinal trajectory organization in a computer-simulated manual welding task. The results showed that spatial welding error decreased most clearly during the earliest stage of practice, with mean absolute lateral error declining from approximately 2.8 mm in the first trial to approximately 1.7 mm by the third trial. This early improvement was then broadly preserved across subsequent sessions. In contrast, smoothness- and fragmentation-related metrics exhibited more variable temporal patterns, indicating that improvements in task-space accuracy were not necessarily accompanied by uniform reorganization of movement dynamics. Associations between spatial error and kinematic features remained limited, suggesting that geometric task accuracy and dynamic trajectory organization represent complementary aspects of simulated manual performance. Overall, the findings show that high-frequency trajectory analysis in VR provides a useful basis for the mathematical modeling of dynamic behavior in simulated welding systems and supports the use of computer simulation for process-level investigation of manual task execution. Full article
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