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Symmetry
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Symmetry in Theoretical and Applied Mechanics
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Symmetry in Theoretical and Applied Mechanics

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

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 12962

Special Issue Editors

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
Dr. Adina Crișan

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

Special Issue Information

Dear Colleagues,

The main purpose of this Special Issue is to encourage researchers to share the latest developments in the field of theoretical and applied mechanics. New formulations are based on vector and homogeneous transformations, matrix exponentials, tensors, and quaternions. Applied kinematics and elastokinematics involve the use of higher-order accelerations. Advanced dynamics uses D’Alembert, Lagrange, Hamilton, Gibbs–Appell, Gauss, and variational equations from analytical mechanics, as well fundamental theorems in Newtonian mechanics. Dynamics and elastodynamics are also based on symmetry and friction types from physical links. For rapid movements, the dynamics studies are extended to higher-order acceleration energies.

Prof. Dr. Iuliu Negrean
Dr. Adina Crișan
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

  • theoretical mechanics
  • applied mechanics
  • analytical dynamics
  • elastokinematics
  • elastodynamics
  • acceleration energies
  • differential principles
  • matrix exponentials
  • tensors
  • quaternions
  • dynamics of multibody systems

Published Papers (6 papers)

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Research

12 pages, 3267 KiB  
Article
The Study of the Dynamic Behavior for a Tamping Rammer
by Radu Mircea Morariu-Gligor
Symmetry 2022, 14(5), 980; https://doi.org/10.3390/sym14050980 - 11 May 2022
Cited by 1 | Viewed by 3958
Abstract
The paper presents a mechanical and a mathematical model, developed by the author for the study of the dynamical behavior of a tamping rammer. At first, some aspects related to the compaction of soil for construction works are presented. In this study, the [...] Read more.
The paper presents a mechanical and a mathematical model, developed by the author for the study of the dynamical behavior of a tamping rammer. At first, some aspects related to the compaction of soil for construction works are presented. In this study, the soil was modeled using the Kelvin–Voigt model. To validate the mathematical model, a program written in C language, that allows to analyze the parameters that influence the operation of the tamping rammer, was developed. Three constructive variants of tamping rammers, following the variation of the displacements of the frame and the sole and the variation of the impact force were analyzed. In the final part, the variation of the studied parameters is illustrated by means of graphical representations. The variation of the studied parameters becomes symmetrical, related to an equilibrium position. Using the application, developed by the author, the variation of the sole and frame displacements, and the variation of the impact force can be traced. The numerical results obtained by running the application, (using three sets of input data), demonstrate the accuracy and the correctness of the proposed mathematical model by analogy with the values provided by the manufacturers. Finally, further research in this field is presented. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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19 pages, 3013 KiB  
Article
New Formulations on Kinetic Energy and Acceleration Energies in Applied Mechanics of Systems
by Iuliu Negrean, Adina Crișan, Florina Șerdean and Sorin Vlase
Symmetry 2022, 14(5), 896; https://doi.org/10.3390/sym14050896 - 27 Apr 2022
Cited by 4 | Viewed by 1446
Abstract
Multibody mechanical systems (i.e., serial, and parallel robots) have a wide range of applications in the industrial field. In technological processes, these systems perform mechanical movements, in which the active forces have a certain time variation law and, hence, induce higher-order accelerations in [...] Read more.
Multibody mechanical systems (i.e., serial, and parallel robots) have a wide range of applications in the industrial field. In technological processes, these systems perform mechanical movements, in which the active forces have a certain time variation law and, hence, induce higher-order accelerations in the mechanical system, which become central functions in acceleration energies. The advanced dynamics study of multibody systems, often characterized by symmetry, is conducted by applying the differential and variational principles. Lagrange–Euler equations and their time derivatives are commonly used. Here, the central function is the kinetic energy and its higher-order time derivatives. Additionally, the generalization of Gibbs–Appell equations, where the central function is represented by the first and higher-order acceleration energy, can be applied. This paper aims to establish a relation between the kinetic energy and acceleration energy for different material systems. This purpose is achieved by applying the absolute second-order time derivative on the expressions of kinetic energy, corresponding to different material systems. Following this differential calculation and by applying some constraints, the relationship between kinetic energy and acceleration energy is obtained. For validating the relation between kinetic energy and acceleration energy of the first, second and third order, an application is presented. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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18 pages, 6920 KiB  
Article
Dynamic Behavior of the Inertial Platform Related to the Research Facility Building Laser and Gamma at ELI-NP Bucharest
by Polidor Bratu, Adrian Mihai Goanta, Nicusor Dragan, Sorin Vlase, Calin Itu, George Lucian Nicolae and Samir Iacovescu
Symmetry 2022, 14(4), 831; https://doi.org/10.3390/sym14040831 - 17 Apr 2022
Cited by 2 | Viewed by 1448
Abstract
This paper aims to study the vibration of the large inertial platform from the Laser + Gamma building that is part of the ELI-NP project. In order to ensure a precisely positioned radiation beam, it is necessary that the shocks and vibrations coming [...] Read more.
This paper aims to study the vibration of the large inertial platform from the Laser + Gamma building that is part of the ELI-NP project. In order to ensure a precisely positioned radiation beam, it is necessary that the shocks and vibrations coming from the external environment are damped or absorbed until they reach the work installations. This is ensured by the platform on which the devices are positioned, a platform that is supported on spring batteries and shock absorbers. A rigid body model is developed in this regard and a comparison with the finite element model of the concrete platform is conducted. It has been found that low vibration modes can be obtained with the help of the rigid model, which also has the advantage of simplicity and very little time is required to obtain results. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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30 pages, 81507 KiB  
Article
CardioVR-ReTone—Robotic Exoskeleton for Upper Limb Rehabilitation following Open Heart Surgery: Design, Modelling, and Control
by Bogdan Mocan, Claudiu Schonstein, Calin Neamtu, Mircea Murar, Mircea Fulea, Radu Comes and Mihaela Mocan
Symmetry 2022, 14(1), 81; https://doi.org/10.3390/sym14010081 - 5 Jan 2022
Cited by 5 | Viewed by 2326
Abstract
Following cardiac surgery, patients experience difficulties with the rehabilitation process, often finding it difficult, and therefore lack the motivation for rehabilitation activities. As the number of people aged 65 and over will rise by 207 percent globally by 2050, the need for cardiac [...] Read more.
Following cardiac surgery, patients experience difficulties with the rehabilitation process, often finding it difficult, and therefore lack the motivation for rehabilitation activities. As the number of people aged 65 and over will rise by 207 percent globally by 2050, the need for cardiac rehabilitation will significantly increase, as this is the main population to experience heart problems. To address this challenge, this paper proposes a new robotic exoskeleton concept with 12 DoFs (6 DoFs on each arm), with a symmetrical structure for the upper limbs, to be used in the early rehabilitation of cardiac patients after open-heart surgery. The electromechanical design (geometric, kinematic, and dynamic model), the control architecture, and the VR-based operating module of the robotic exoskeleton are presented. To solve the problem of the high degree of complexity regarding the CardioVR-ReTone kinematic and dynamic model, the iterative algorithm, kinetic energy, and generalized forces were used. The results serve as a complete model of the exoskeleton, from a kinematic and dynamic point of view as well as to the selection of the electric motors, control system, and VR motivation model. The validation of the concept was achieved by evaluating the exoskeleton structure from an ergonomic point of view, emphasizing the movements that will be part of the cardiac rehabilitation. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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15 pages, 1295 KiB  
Article
Approximation Solution of the Nonlinear Circular Sitnikov Restricted Four–Body Problem
by Reena Kumari, Ashok Kumar Pal, Elbaz I. Abouelmagd and Sawsan Alhowaity
Symmetry 2021, 13(10), 1966; https://doi.org/10.3390/sym13101966 - 18 Oct 2021
Cited by 11 | Viewed by 1357
Abstract
In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated [...] Read more.
In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt–Poincaré method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt–Poincaré method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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17 pages, 645 KiB  
Article
Exact Closed-Form Solutions of the Motion in Non-Inertial Reference Frames, Using the Properties of Lie Groups SO3 and SE3
by Daniel Condurache and Eugen Șfartz
Symmetry 2021, 13(10), 1963; https://doi.org/10.3390/sym13101963 - 18 Oct 2021
Cited by 1 | Viewed by 1638
Abstract
The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group [...] Read more.
The paper offers a general symbolic method to study the motion in a non-inertial reference frame. In order to achieve this, we use the algebraic and geometric properties of the Lie group of special orthogonal tensors, SO3, and the Lie group of the rigid body displacements, SE3. We obtain a simplified form of the initial value problem that models the non-inertial motion using a tensor instrument introduced in this paper. Thus, the study of the motion in a non-inertial reference frame is transferred into the study of a classical motion in an inertial reference frame. The applications of this method refer to solving the relative motion problem and deriving the straightforward solution to classical theoretical mechanics problems. The motion in a uniform gravitational force field in a rotating reference frame, the motion of a charged particle in non-stationary electric and magnetic fields, the exact solution of the relative rigid body motion in the non-inertial reference frame are studied. Using this symbolic method in studying the motion in a non-inertial reference frame reduces the number of computations. In addition, it offers, in some essential particular cases, exact closed-form coordinate-free analytical solutions. Full article
(This article belongs to the Special Issue Symmetry in Theoretical and Applied Mechanics)
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