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Symmetry
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Advances in Mechanics and Control
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Advances in Mechanics and Control

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

Deadline for manuscript submissions: closed (10 October 2022) | Viewed by 33177

Special Issue Editors

Prof. Dr. Yury Razoumny

E-Mail Website
Guest Editor
Department of Mechanics and Control Processes, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
Interests: mathematic modelling; astrodynamics; system analysis; aerospace systems; space flight mechanics; satellite constellation; orbital dynamics; space debris; on-orbit servicing
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Arun K. Misra

E-Mail Website
Guest Editor
Department of Mechanical Engineering, McGill University, Montreal, QC H3A 0C3, Canada
Interests: satellite dynamics and control; space robotics; dynamics of aerospace structures; active space debris removal using robots; dynamics of tethered space systems; spacecraft motion in the vicinity of asteroids; formation flying of satellites; space elevator
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Renuganth Varatharajoo

E-Mail Website
Guest Editor
Department of Aerospace Engineering, Universiti Putra Malaysia, Seri Kembangan, Selangor, Malaysia
Interests: aerospace engineering
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Sergei A. Kupreev

E-Mail
Guest Editor
Department of Mechanics and Mechatronics, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia Federation
Interests: space flight mechanics; orbital maneuvering; space debris
Dr. Maksim Karatunov

E-Mail Website
Co-Guest Editor
Department of Mechanics and Control Processes, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
Interests: space situational awareness; space debris; orbital transfers and spacecraft control; astrodynamics; Newtonian dynamics
Dr. Vladimir Razoumny

E-Mail Website
Co-Guest Editor
Department of Mechanics and Control Processes, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 117198 Moscow, Russia
Interests: on-orbit servicing; orbital transfers and spacecraft control; space flight mechanics; space systems design

Special Issue Information

Dear Colleagues,

The key factor of creation efficient optimization methods in mechanics and control is revealing the regularities in complex technical and nature processes and provides them for analytical and numerical–analytical modeling. The level of penetration into the black box of this phenomenon could be estimated by the level of symmetry in its mathematical description. Papers devoted to research on the regularities of complex phenomena in mechanics and control using neurotechnology, machine learning, other up-to-date mathematical instruments and information technology are most welcome. Applications are planned to be in aerospace as a recommended area, including its connected fields. We solicit contributions for the relevant problems of space mission and system design, satellite constellation and formation flying, space traffic management, space debris removal, aerospace robotic vehicle control, Earth remote sensing, and geoinformation systems. We would like to invite domestic and foreign experts to contribute their research by employing the symmetry or asymmetry concept in the methods and methodologies, including but not limited to:

  • Mechanics and control
  • Neurotechnology and machine learning
  • Space mission and system design
  • Satellite constellation and formation flying
  • Space traffic management
  • Space debris removal
  • Aerospace robotic vehicles control
  • Earth remote sensing and geoinformation systems.

Prof. Dr. Yury Razoumny
Prof. Dr. Arun K. Misra
Prof. Dr. Renuganth Varatharajoo
Prof. Dr. Sergei A. Kupreev
Guest Editors

Dr. Maksim Karatunov
Dr. Vladimir Razoumny
Co-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

  • mechanics and control
  • neurotechnology and machine learning
  • space mission and system design
  • satellite constellation and formation flying
  • space traffic management
  • space debris removal
  • aerospace robotic vehicles control
  • earth remote sensing and geoinformation systems

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Published Papers (17 papers)

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Editorial

Jump to: Research

5 pages, 188 KiB  
Editorial
Special Issue: Advances in Mechanics and Control
by Antonio Fernando Bertachini de Almeida Prado
Symmetry 2023, 15(1), 141; https://doi.org/10.3390/sym15010141 - 3 Jan 2023
Viewed by 916
Abstract
The topic of mechanics and control is very important nowadays, with many applications in several fields, such as space research and the modeling of viruses [...] Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)

Research

Jump to: Editorial

17 pages, 3409 KiB  
Article
A Gain Scheduling Design Method of the Aero-Engine Fuel Servo Constant Pressure Valve with High Accuracy and Fast Response Ability
by Wenshuai Zhao, Xi Wang, Zhen Jiang and Yifu Long
Symmetry 2023, 15(1), 45; https://doi.org/10.3390/sym15010045 - 24 Dec 2022
Cited by 2 | Viewed by 1524
Abstract
Constant pressure valve, which has an axially symmetric structure, is an essential component to supply the servo reference pressure for aero-engine hydraulic mechanical control systems, and its performance directly impacts the performance of the control system. This paper constructs a closed-loop disturbance rejection [...] Read more.
Constant pressure valve, which has an axially symmetric structure, is an essential component to supply the servo reference pressure for aero-engine hydraulic mechanical control systems, and its performance directly impacts the performance of the control system. This paper constructs a closed-loop disturbance rejection system of the constant pressure valve based on the linear incremental description method, in which the controlled object is the controlled pressure, and the stabilization controller is constructed by the closed-loop feedback motion valve. Meanwhile, the linear models of the closed-loop system are calculated. Subsequently, based on the bode frequency domain characteristic analysis, the accurate influences of the stabilization control gain on the dynamic performance and stability of the system are given. On this basis, a gain scheduling design method of the system is proposed, and the geometry design and implementation method of the inlet orifice is proposed to complete the design work. The simulation results show that under bad conditions, which include the 1 MPa strong step disturbance of the inlet pressure and the step disturbance of the variable outlet flow area, the steady-state working range of the controlled pressure is 1.5 ± 0.01 MPa, the steady-state error is not more than 0.7%, and the regulation time is not more than 0.006 s. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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13 pages, 719 KiB  
Article
Assessing Parameters of the Coplanar Components of Perturbing Accelerations Using the Minimal Number of Optical Observations
by Andrey Baranov, Vladimir Agapov, Natalya Golosova and Maksim Karatunov
Symmetry 2022, 14(12), 2564; https://doi.org/10.3390/sym14122564 - 5 Dec 2022
Cited by 2 | Viewed by 1092
Abstract
The method presented in this paper is developed to assess the parameters (the application moment and the magnitude of a velocity impulse) of a maneuver-like perturbation of motion of the center of mass of a spacecraft in a near-circular orbit. The assessment is [...] Read more.
The method presented in this paper is developed to assess the parameters (the application moment and the magnitude of a velocity impulse) of a maneuver-like perturbation of motion of the center of mass of a spacecraft in a near-circular orbit. The assessment is based on the information on the spacecraft’s trajectory before the maneuver and the optical observations of the spacecraft’s angular position (right ascension and declination angles) after the maneuver. This study considers the cases of solely transversal (in-track) or transversal and radial components of the velocity increment vector. A single pair of the values of angles is used for the assessment of the single transversal maneuver parameters and two pairs are used in the other cases. The method also makes it possible to estimate the parameters of a continuous maneuver performed with low-thrust engines. For this case the property of its symmetry is used. The approach described in this article makes it possible to determine the spacecraft’s orbit after the maneuver much faster and more accurately in comparison to traditional methods. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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13 pages, 11717 KiB  
Article
Lifetimes of an Exomoon Orbiting a Jupiter-Like Planet in a Double Star System with the Mass of the Sun
by Allan Kardec de Almeida Junior, Vivian M. Gomes and Antonio Fernando Bertachini de Almeida Prado
Symmetry 2022, 14(10), 2001; https://doi.org/10.3390/sym14102001 - 24 Sep 2022
Cited by 1 | Viewed by 1676
Abstract
The search for life outside Earth has been a popular topic for a long time in the scientific literature, but it gained more possibilities with the discovery of planets around other stars besides our Sun. In this sense, similarly to what happens in [...] Read more.
The search for life outside Earth has been a popular topic for a long time in the scientific literature, but it gained more possibilities with the discovery of planets around other stars besides our Sun. In this sense, similarly to what happens in our Solar System, moons of planets sometimes offer good conditions for life if stable orbits for those moons exist. Thus, the present paper analyzes a system composed of a moon (with the mass of the Earth) orbiting a planet (with the mass of Jupiter), which is orbiting a double star system (whose total mass is equal to the mass of the Sun). It is an important topic because there is a large proportion of double stars in the universe. The initial conditions are given by a symmetric configuration of two circular orbits. Although this symmetry is broken due to the four body dynamics, the conditions in which the moon remains bound with the planet are investigated. The stability of the system is given by the survival of the orbit of the moon for an integration time of the order of 10,000 revolutions of the satellite around its mother planet. The regions of stable, unstable, and collision orbits are mapped, and empirical linear equations that separate those regions are obtained from the maps. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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21 pages, 4055 KiB  
Article
Searching for Orbits for a Mission to the Asteroid 2001SN263 Considering Errors in the Physical Parameters
by Allan Kardec de Almeida Junior, Bruna Yukiko Pinheiro Masago Mescolotti, Ana Paula Marins Chiaradia, Vivian M. Gomes and Antonio Fernando Bertachini de Almeida Prado
Symmetry 2022, 14(9), 1789; https://doi.org/10.3390/sym14091789 - 28 Aug 2022
Cited by 1 | Viewed by 1473
Abstract
The main goal of this paper is to search for orbits that can be used in the Brazilian proposed Aster mission. This mission is under study and its objective is to use a spacecraft to observe the system 2001SN263, which is [...] Read more.
The main goal of this paper is to search for orbits that can be used in the Brazilian proposed Aster mission. This mission is under study and its objective is to use a spacecraft to observe the system 2001SN263, which is a triple asteroid system. With respect to the two-body problem (spacecraft and the main asteroid), the symmetries of the orbits are broken by the oblateness of the main body of the system, the solar radiation pressure, and the gravitational attraction of the two moons of the main body. Additionally, the masses of these two moons have errors associated with their predicted values, which reinforce the asymmetry and require extra effort to maintain the observational objectives of the mission. The idea is to find orbits that remain for some time observing the three bodies of that system, even if the physical parameters of the bodies are not the ones expected from observations made from the Earth. This is accomplished by studying the effects of errors in all the physical properties of the three asteroids in the trajectories described by a spacecraft that is orbiting this system. Several important and useful trajectories are found, which are the ones that can observe the desired bodies, even if the physical parameters are not the expected ones. To express our results, we built time histories of the relative distances between each of the asteroids and the spacecraft. They are used to select the trajectories according to the amount of time that we need to observe each body of the system. In this way, the first objective of this research is to search for trajectories to keep the spacecraft close to the three bodies of the system as long as possible, without requiring orbital maneuvers. The errors for the masses of the two smaller and lesser known bodies are taken into consideration, while the mass of the most massive one is assumed to be known, because it was determined with higher precision by observations. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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23 pages, 15034 KiB  
Article
Low Thrust Propelled Close Approach Maneuvers
by Alessandra F. S. Ferreira, Antonio Elipe, Rodolpho V. De Moraes, Antônio F. B. A. Prado, Othon C. Winter and Vivian M. Gomes
Symmetry 2022, 14(9), 1786; https://doi.org/10.3390/sym14091786 - 27 Aug 2022
Cited by 2 | Viewed by 1689
Abstract
The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a “gravity assisted” maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the [...] Read more.
The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a “gravity assisted” maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the gravity of this body to change its trajectory. This approach trajectory has symmetry with respect to the periapsis line when observed from a reference frame fixed in the approached body. There is also a more complex maneuver, when the passage by the celestial body is combined with the application of propulsion, either to give extra energy to the spacecraft or to help to satisfy other constraints required by the mission, like passing by a giving point or region in space. The main object of this study is to measure the efficiency of the application of a continuous thrust combined with the “gravity assisted” maneuver. The effect of this combination is analyzed using maps that give the energy variation of the spacecraft as function of the parameters related to the maneuver. This analysis is made from the point of view of the variation of energy of the spacecraft with respect to the main body of the system. The continuous thrust is applied in the different regions of the trajectory to evaluate the effects of the locations of the thrusting arcs in the variations of energy. The effects of the variations of the direction of the thrust are also studied. This type of combined maneuver may be used to give extra energy to the spacecraft and keeping control of the trajectory during the close approach to better position the spacecraft to complete the mission. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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16 pages, 1034 KiB  
Article
Deflecting an Asteroid on a Collision Course with Earth Using a Powered Swing-By Maneuver
by Bruno S. Chagas, Antonio Fernando Bertachini de Almeida Prado and Othon Cabo Winter
Symmetry 2022, 14(8), 1658; https://doi.org/10.3390/sym14081658 - 11 Aug 2022
Cited by 3 | Viewed by 2079
Abstract
The deflection of potentially dangerous asteroids has been treated with great intensity and has gained more and more attention in scientific research. Different techniques are developed over the years. Among these techniques, we found the kinetic impact deflection technique to be the most [...] Read more.
The deflection of potentially dangerous asteroids has been treated with great intensity and has gained more and more attention in scientific research. Different techniques are developed over the years. Among these techniques, we found the kinetic impact deflection technique to be the most viable at the moment. In this work we address the kinetic impact deflection technique, but in a scenario where we have a short time to deflect an asteroid that will collide with Earth. For this, we also use a maneuver similar to a powered gravity-assisted maneuver with Earth in a previous passage to change the trajectory of the asteroid to avoid the collision. We apply this technique in three scenarios: (i) impulse before the close encounter, (ii) impulse during the close encounter, and (iii) impulse after the close encounter. We observe that some trajectories are symmetric with respect to the line Sun–Earth, and others are asymmetric. We show that, using this technique, it is possible to change the trajectory of the asteroid, even in a short period, to avoid the collision without using a large variation of velocity in the orbit of the asteroid. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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19 pages, 5561 KiB  
Article
Mapping Natural Orbits around Io
by Thamis C. F. Carvalho Ferreira, Antonio F. Bertachini A. Prado, Silvia M. Giuliatti Winter and Lucas S. Ferreira
Symmetry 2022, 14(7), 1478; https://doi.org/10.3390/sym14071478 - 19 Jul 2022
Cited by 7 | Viewed by 1877
Abstract
As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural [...] Read more.
As the most volcanically active celestial body in the Solar System, Io is a natural satellite of Jupiter due to its proximity to the planet and the fact that it is in mean motion resonance, known as the Laplace resonance, with the natural satellites Europa and Ganymede. This natural satellite is a good candidate to be visited by future missions. In this sense, the present work has the goal of studying and mapping the best initial orbital conditions for orbits around Io, considering the symmetrical or asymmetical perturbative effects of a third body (Jupiter) and the J2 term from the mass configuration of Io. The initial orbital parameters of the probe were investigated through a set of numerical simulations. The results showed that although most orbits around Io have lifetimes of less than 6 months, some regions were found where the initial conditions of the orbits provided satisfactory times for the accomplishment of future missions around Io. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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14 pages, 1548 KiB  
Article
Deployment and Retrieval Missions from Quasi-Periodic and Chaotic States under a Non-Linear Control Law
by Francisco J. T. Salazar and Antonio B. A. Prado
Symmetry 2022, 14(7), 1381; https://doi.org/10.3390/sym14071381 - 5 Jul 2022
Cited by 5 | Viewed by 1396
Abstract
When the length of the tether remains constant, the relative planar motion of the tethered subsatellite with respect to the base satellite in a circular orbit around the Earth, is similar to a simple pendulum motion, i.e., there are two kinds of equilibrium [...] Read more.
When the length of the tether remains constant, the relative planar motion of the tethered subsatellite with respect to the base satellite in a circular orbit around the Earth, is similar to a simple pendulum motion, i.e., there are two kinds of equilibrium points: local vertical and local horizontal positions, which are center and saddle points, respectively. However, when out-of-plane motion is initially excited, the relative motion of the subsatellite presents symmetric quasi-periodic and chaotic behavior. In the first part of this study, such trajectories are analyzed by means of Poincaré sections. In the second part, a non-linear tension force by using a Lyapunov approach is proposed for controlling the coupled pitch-roll motion during the deployment and retrieval phases. The goal of this paper is to guide the relative non-linear motion of the subsatellite to the local upward vertical position. The numerical results show that the non-linear tension control steered the subsatellite close to the local vertical direction very well, reducing the quasi-periodic and chaotic oscillations. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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25 pages, 5431 KiB  
Article
Lifetime and Dynamics of Natural Orbits around Titan
by Lucas S. Ferreira, Rafael Sfair and Antônio F. Bertachini A. Prado
Symmetry 2022, 14(6), 1243; https://doi.org/10.3390/sym14061243 - 15 Jun 2022
Cited by 8 | Viewed by 2440
Abstract
Considering the growing interest in sending probes to the natural satellite Titan, our work aims to investigate and map natural orbits around this moon. For that, we use mathematical models with forces that have symmetry/asymmetry phenomena, depending on the force, applied to orbits [...] Read more.
Considering the growing interest in sending probes to the natural satellite Titan, our work aims to investigate and map natural orbits around this moon. For that, we use mathematical models with forces that have symmetry/asymmetry phenomena, depending on the force, applied to orbits around Titan. We evaluated the effects due to the gravitational attraction of the Saturn, together with the perturbative effects coming from the non-sphericity of Titan (the gravitational coefficient J2) and the effects of the atmospheric drag present in the natural satellite. Lifetime maps were generated for different initial configurations of the orbit of the probe, which were analyzed in different scenarios of orbital perturbations. The results showed the existence of orbits surviving at least 20 years and conditions with shorter times, but sufficient to carry out possible missions, including the important polar orbits. Furthermore, the investigation of the oscillation rate of the altitude of the probe, called coefficient Δ, proposed in this work, showed orbital conditions that result in more minor oscillations in the altitude of the spacecraft. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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24 pages, 4873 KiB  
Article
An Enhanced Calculation Method of the Heat Rejection System of a Free-Piston Stirling Engine (FPSE) Operating on the Moon
by Sergey Smirnov, Mikhail Sinkevich, Yuri Antipov, Igor Tsarkov, Sergei Kupreev and Hassan Khalife
Symmetry 2022, 14(6), 1168; https://doi.org/10.3390/sym14061168 - 6 Jun 2022
Cited by 2 | Viewed by 2232
Abstract
In this paper, an enhanced calculation method of a heat rejection system operating on the moon is presented. This was taken into consideration in the developed calculation method and in the propagation of heat fluxes with the radiation of the removed heat. The [...] Read more.
In this paper, an enhanced calculation method of a heat rejection system operating on the moon is presented. This was taken into consideration in the developed calculation method and in the propagation of heat fluxes with the radiation of the removed heat. The developed method made it possible to effectively evaluate the capabilities of various refrigerants and choose the radiator parameters and the refrigerant flow regime in a less time-consuming process and with minimal deviations (<5%) compared to the previously developed two-dimensional radiator model by the authors. A comparative analysis was carried out for two refrigerants: helium and liquid ammonia. It has been established that when using liquid ammonia, there are more possibilities for varying the geometric parameters of the radiator. The use of liquid ammonia as a refrigerant made it possible to reduce the power spent on pumping the refrigerant through the radiator. Using helium, the power for pumping the refrigerant was NR= 5.1 W during a turbulent flow Re = 4500. On the other hand, the power for pumping liquid ammonia was NR= 0.27 W. In addition, using liquid ammonia increased the heat flux radiated by the radiator pipe by 3.9 times, which made it to possible to increase the fin width and reduce the length of the radiator pipe. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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21 pages, 6761 KiB  
Article
Trajectories Derived from Periodic Orbits around the Lagrangian Point L1 and Lunar Swing-Bys: Application in Transfers to Near-Earth Asteroids
by Rebeca S. Ribeiro, Cristiano F. de Melo and Antônio F. B. A. Prado
Symmetry 2022, 14(6), 1132; https://doi.org/10.3390/sym14061132 - 31 May 2022
Cited by 3 | Viewed by 2277
Abstract
To present a set of trajectories derived from the retrograde periodic orbits around the Lagrangian equilibrium point L1, this paper considers the Circular Restricted Three-body Problem with Earth-Moon masses (CR3BP), the Restricted Bicircular, and Full Four-Body Sun-Earth-Moon-spacecraft Problems (BCR4BP and FR4BP, [...] Read more.
To present a set of trajectories derived from the retrograde periodic orbits around the Lagrangian equilibrium point L1, this paper considers the Circular Restricted Three-body Problem with Earth-Moon masses (CR3BP), the Restricted Bicircular, and Full Four-Body Sun-Earth-Moon-spacecraft Problems (BCR4BP and FR4BP, respectively). These periodic orbits are predicted by the dynamics of the CR3BP. To generate the trajectories of this set, first, slightly different increments of velocity (∆Vs) from those needed to generate periodic orbits around L1 are applied to a spacecraft in circular low Earth orbits in the same direction of their motion when the Earth, the spacecraft, and the Moon are aligned in this order. Thus, translunar trajectories derived from the periodic orbits are obtained and they will lead the spacecraft to the vicinity of the Moon. Depending on the values of the |∆Vs|, which are also functions of the relative positioning between the Sun, the Earth, and the Moon, three types of trajectories of interest are found: Collision with the Moon, escape, and geocentric orbits with large semi-major axes. For a well-defined interval of the |∆Vs|, the trajectories accomplish swing-bys with the Moon and obtain energy to escape from the Earth–Moon system and reach Near-Earth Asteroids (NEAs) between the orbits of Venus and Mars. This procedure reduces the costs of inserting spacecraft into transfer trajectories to a set of NEAs in terms of the required |∆V| by up to 5% when compared to Lambert’s problem, for example. This work also presents analyses of examples of transfers to the NEAs 3361 Orpheus, 99942 Apophis, and 65803 Didymos, from 2025 on. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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10 pages, 2773 KiB  
Article
A Comparative Analysis of Different Strains of Coronavirus Based on Genometric Mappings
by Ivan V. Stepanyan and Michail Y. Lednev
Symmetry 2022, 14(5), 942; https://doi.org/10.3390/sym14050942 - 5 May 2022
Cited by 5 | Viewed by 1703
Abstract
Coronaviruses are viruses that infect the respiratory system of humans. Besides high mortality rates among the population, they brought about several economic crises on a global scale. Methods. To study and identify features in the genetic composition of the nucleotide sequences of [...] Read more.
Coronaviruses are viruses that infect the respiratory system of humans. Besides high mortality rates among the population, they brought about several economic crises on a global scale. Methods. To study and identify features in the genetic composition of the nucleotide sequences of various coronaviruses, we applied copyright algorithms and visualization, which allowed us to compare the biochemical parameters of diverse RNA coronaviruses in a visual form. Results. The article provides examples of different approaches to imaging coronaviruses. We have provided examples of coronavirus RNA structure visualization in various parametric spaces (1-D and 2-D). We employed various visualization types, including structural, integral, and frequency. The research discussed methods of visualization. Our team developed visualization and comparative analysis of coronavirus serotypes and visualization of SARS-CoV-2 coronavirus datasets. Discussion followed on the visualization results. The presented techniques and the results allowed for displaying the structure of RNA sequences of coronaviruses in spaces of various dimensions. Conclusions. According to our findings, the proposed method contributes to the visualization of the genetic coding of coronaviruses. We discussed the issues of machine learning and neural network technology concerning the analysis of coronaviruses based on the presented approach. The described line of research is essential for the study and control of complex quantum mechanical systems, such as RNA or DNA. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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13 pages, 4414 KiB  
Article
Spectral Decomposition of Mappings of Molecular Genetic Information in the System Basis of Single Nucleotide Functions
by Ivan Stepanyan and Michail Lednev
Symmetry 2022, 14(5), 844; https://doi.org/10.3390/sym14050844 - 19 Apr 2022
Cited by 6 | Viewed by 1486
Abstract
This paper presents and visualizes examples of large amounts of genetic information using a new class of cognitive computer graphics algorithms. These algorithms are related to the semiotics of perception and allow the interpretation of those properties of nucleotide sequences that are difficult [...] Read more.
This paper presents and visualizes examples of large amounts of genetic information using a new class of cognitive computer graphics algorithms. These algorithms are related to the semiotics of perception and allow the interpretation of those properties of nucleotide sequences that are difficult to perceive by simple reading or by standard means of statistical analysis. This article summarizes previously presented algorithms for visualizing long nucleic acids based on the primary Hadamard–Walsh function system. The described methods allow us to produce one-dimensional mappings of nucleic acids by levels corresponding to their scale-integral physicochemical parameters and construct a spectral decomposition of the nucleotide composition. An example of the spectral decomposition of parametric representations of molecular genetic structures is given. In addition, a multiscale composition of genetic functional mappings visualizing the structural features of nucleic acids is discussed. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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25 pages, 3203 KiB  
Article
Mapping Long-Term Natural Orbits about Titania, a Satellite of Uranus
by Jadilene Xavier, Antônio Bertachini Prado, Silvia Giuliatti Winter and Andre Amarante
Symmetry 2022, 14(4), 667; https://doi.org/10.3390/sym14040667 - 24 Mar 2022
Cited by 6 | Viewed by 2225
Abstract
Close polar and circular orbits are of great interest for the exploration of natural satellites. There are still no studies in the literature investigating orbits around Titania, the largest satellite of Uranus. In this work, we present results of a set of numerical [...] Read more.
Close polar and circular orbits are of great interest for the exploration of natural satellites. There are still no studies in the literature investigating orbits around Titania, the largest satellite of Uranus. In this work, we present results of a set of numerical simulations carried out to obtain long-duration orbits for a probe around Titania. Through an expansion of the gravitational potential up to second order, the asymmetry of the gravitational field due to Titania’s coefficient C22, the zonal coefficient J2, and the gravitational perturbation of Uranus is considered. The analysis of lifetime sensitivity due to possible errors in the values of J2 and C22 is investigated using multiple regression models. Simulations were performed for different eccentricity values, and lifetime maps were constructed. The results show that low-altitude and near-circular orbits have longer lifetimes due to the balance between the disturbance of Uranus and the gravitational coefficients of Titania. The results also show that non-zero values of the longitude of periapsis (ω) and longitude of the ascending node (Ω) are essential to increase the lifetime up to eight times compared to cases where ω=Ω=0∘. We also show that an orbit with eccentricity 10−3 is the most affected by errors in the values of J2 and C22. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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38 pages, 3936 KiB  
Article
Swing-By Applications and Estimation of the Van Allen Belts’ Radiation Exposure for a Spacecraft in a Low Thrust Transfer to the Moon
by Rodrigo N. Schmitt, Antonio F. B. A. Prado, Alexander Sukhanov and Vivian M. Gomes
Symmetry 2022, 14(3), 617; https://doi.org/10.3390/sym14030617 - 19 Mar 2022
Cited by 2 | Viewed by 2670
Abstract
This paper presents a handful of the underlying properties of a spacecraft’s transfer from a low Earth orbit (LEO) to the moon’s orbit using an electric propulsion (low-thrust) system. The use of analytical and numerical-analytical modeling in complex natural and technical processes is [...] Read more.
This paper presents a handful of the underlying properties of a spacecraft’s transfer from a low Earth orbit (LEO) to the moon’s orbit using an electric propulsion (low-thrust) system. The use of analytical and numerical-analytical modeling in complex natural and technical processes is a key factor in this issue of Symmetry, which has been thoroughly explored in this paper. First, an optimization problem was considered to find the locations and lengths of the thrust arcs that maximizes the final mass of the spacecraft for a number of transfer orbits, thereby limiting the scope of trajectories to the most fuel-efficient ones. In addition to this, the Van Allen belts were modelled according to the density of electrons and protons in each point of space, in order to measure the total radiation absorbed by the spacecraft through an integration of the density of particles over the corresponding time. The simulations were then able to predict the relationship between the fluence of the particles and several initial parameters, such as the initial orbit’s eccentricity and the propulsion system’s characteristics. Then, a multi-linear regression and an artificial neural network were fitted to the data through a regression that related the fluence of protons and electrons as a function of the following parameters: mission time, specific impulse, thrust, final mass (i.e., propellant consumption) and the initial height of the perigee, eccentricity and inclination. This analysis was proven to be powerful due to the expressive values from statistical tests, showing underlying positive correlations between thrust, mission time and final spacecraft mass with the fluence of particles, and negative correlations between specific impulse, initial orbit eccentricity, inclination and the height of the perigee with the fluence of particles. Finally, an analysis of a swing-by maneuver was also carried out, together with the radiation incidence, revealing hidden dependencies of the increments in energy and velocity with respect to the fuel consumption, radiation absorption, propulsion system and initial orbit parameters. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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14 pages, 1987 KiB  
Article
Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry
by Vladimir Aristov and Ivan Stepanyan
Symmetry 2022, 14(3), 505; https://doi.org/10.3390/sym14030505 - 1 Mar 2022
Cited by 5 | Viewed by 2449
Abstract
We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. [...] Read more.
We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erdőos-Rényi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems. Full article
(This article belongs to the Special Issue Advances in Mechanics and Control)
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