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Symmetry
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Symmetry in the Advanced Mechanics of Systems
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Symmetry in the Advanced Mechanics of Systems

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

Deadline for manuscript submissions: closed (31 May 2024) | Viewed by 2204

Special Issue Editors

Dr. Adina Crișan

E-Mail Website
Guest Editor
Associate Professor, Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
Interests: advanced kinematics; advanced dynamics; analytical dynamics; dynamic accuracy; applied mechanics; advanced mechanics in robotics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Iuliu Negrean

E-Mail Website
Guest Editor
Department of Mechanical Systems Engineering, Faculty of Machine Building, Technical University of Cluj-Napoca, 400641 Cluj-Napoca, Romania
Interests: advanced kinematics; advanced dynamics; analytical dynamics; dynamic accuracy; applied mechanics; advanced mechanics in robotics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

“Symmetry in the Advanced Mechanics of Systems” refers, on the one hand, to advanced kinematics and elastokinematics and, on the other hand, to the advanced dynamics and elastodynamics of multibody systems. Among these, an essential role is having the rigid and elastic structure of serial, parallel and mobile robots, taking compulsorily into consideration the holonomic, nonholonomic and critical mechanical features.

In the symmetry of advanced kinematics and elastokinematics, besides the classical models concerning the relative movement of mechanical systems, is the compulsory application of novel models based on matrix exponentials, quaternions, higher-order differential matrices, higher-order polynomial interpolation functions and higher-order linear and angular accelerations typical of fast-moving holonomic, nonholonomic and critical mechanical systems.

In the symmetry of advanced dynamics and elastodynamics, alongside the fundamental notions and theorems typical to Newtonian dynamics, it is compulsory to conduct research oriented around the differential and variational principles from analytical dynamics (Lagrange equations of the first and second kind, Hamilton equations and Appell equations), an essential role allowing for the application of higher-order polynomial interpolation functions, higher-order acceleration energies, generalized dynamic forces, impact of dynamics and differential equations of higher order corresponding to the fast movements of holonomic, nonholonomic and critical systems, taking into account the compulsory topic of the type of frictions developed in physical links. As a result, the research can also be in regards to novel mathematical models corresponding to symmetry in the dynamic accuracy of mechanical systems.

The main purpose of this Special Issue is to encourage researchers to share the latest developments in the field of symmetry in advanced kinematics and dynamics of systems, analytical dynamics of multibody systems and robotics.

Dr. Adina Crișan
Prof. Dr. Iuliu Negrean
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • advanced kinematics
  • matrix exponentials
  • quaternions
  • polynomial interpolation functions
  • Newtonian dynamics
  • fundamental theorems of dynamics
  • advanced dynamics
  • differential principles
  • acceleration energies
  • analytical dynamics
  • dynamic accuracy
  • applied mechanics
  • robotics

Published Papers (2 papers)

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Research

91 pages, 28724 KiB  
Article
PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process
by Ming Li
Symmetry 2024, 16(5), 635; https://doi.org/10.3390/sym16050635 - 20 May 2024
Viewed by 390
Abstract
This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of [...] Read more.
This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research. Full article
(This article belongs to the Special Issue Symmetry in the Advanced Mechanics of Systems)
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33 pages, 6793 KiB  
Article
Mathematical Modeling of Robotic Locomotion Systems
by Erik Prada, Ľubica Miková, Ivan Virgala, Michal Kelemen, Peter Ján Sinčák and Roman Mykhailyshyn
Symmetry 2024, 16(3), 376; https://doi.org/10.3390/sym16030376 - 20 Mar 2024
Viewed by 1285
Abstract
This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of symmetrical [...] Read more.
This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of symmetrical locomotion systems and their control and motion planning. These methods are based on extracting the symmetries of Lie groups from the locomotion system in order to simplify the resulting equations. In the second section, the special two-dimensional Euclidean group SE2 and its splitting into right and left actions are derived. The physical interpretation of the local group and spatial velocities is investigated, and by virtue of the fact that both of these velocities represent the same velocity from a physical point of view, the dependence between them can be found by means of the adjoint action. The third section is devoted to the modeling and analysis of the planar locomotion of the symmetrical serpentine robot; the positions and local group velocities of its links are derived, the vector fields for the local connections are given, and the trajectories of the individual variables in the lateral movement of the kinematic snake are shown. At the end of the article, the overall benefits of the scientific study are summarized, as is the comparison of the results from the simulation phase, while the most significant novelty compared to alternative publications in the field can be considered the realization of this study with a description of the relevant methodology at a detailed level; that is, the locomotion results confirm the suitability of the use of geometric mechanics for these symmetrical locomotion systems with nonholonomic constraints. Full article
(This article belongs to the Special Issue Symmetry in the Advanced Mechanics of Systems)
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