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Keywords = restricted four–body problem

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14 pages, 290 KB  
Article
Noncollision Periodic Solutions for Circular Restricted Planar Newtonian Four-Body Problems
by Xiaoxiao Zhao, Liang Ding and Shiqing Zhang
Mathematics 2025, 13(18), 3015; https://doi.org/10.3390/math13183015 - 18 Sep 2025
Viewed by 256
Abstract
We study a class of circular restricted planar Newtonian four-body problems in which three masses are positioned at the vertices of a Lagrange equilateral triangle configuration, each mass revolving around the center of mass in circular orbits. Assuming that the value of the [...] Read more.
We study a class of circular restricted planar Newtonian four-body problems in which three masses are positioned at the vertices of a Lagrange equilateral triangle configuration, each mass revolving around the center of mass in circular orbits. Assuming that the value of the fourth mass is negligibly small (i.e., it does not perturb the motion of the other three masses, though its own motion is influenced by them), we use variational minimization methods to prove the existence of noncollision periodic solutions with some fixed winding numbers. These noncollision solutions exist for both equal and unequal mass values for the three bodies located at the vertices of the Lagrange equilateral configuration. Full article
(This article belongs to the Section E4: Mathematical Physics)
12 pages, 2049 KB  
Article
Functional Independence of Taiwanese Children with Silver–Russell Syndrome
by Hung-Hsiang Fang, Chung-Lin Lee, Chih-Kuang Chuang, Huei-Ching Chiu, Ya-Hui Chang, Yuan-Rong Tu, Yun-Ting Lo, Jun-Yi Wu, Yen-Yin Chou, Chung-Hsing Wang, Shio-Jean Lin, Shao-Yin Chu, Chen Yang, Tsung-Ying Ou, Hsiang-Yu Lin and Shuan-Pei Lin
Diagnostics 2025, 15(9), 1109; https://doi.org/10.3390/diagnostics15091109 - 27 Apr 2025
Viewed by 1886
Abstract
Background: Silver–Russell syndrome (SRS) is a genetic disorder characterized by prenatal and postnatal growth retardation. Affected individuals commonly present with low birth weight, intrauterine growth restriction, postnatal short stature, hemihypotrophy, characteristic facial features, and body asymmetry. Methods: This study includes 24 Taiwanese children [...] Read more.
Background: Silver–Russell syndrome (SRS) is a genetic disorder characterized by prenatal and postnatal growth retardation. Affected individuals commonly present with low birth weight, intrauterine growth restriction, postnatal short stature, hemihypotrophy, characteristic facial features, and body asymmetry. Methods: This study includes 24 Taiwanese children with SRS aged 2 years to 13 years and 3 months who were recruited at MacKay Memorial Hospital and other Taiwan hospitals between January 2013 and December 2024. Functional independence was assessed using the Functional Independence Measure for Children (WeeFIM) to evaluate self-care, mobility, and cognition domains. Results: The mean total WeeFIM score was 106.9 ± 23.2 (range: 54–126), with mean self-care, mobility, and cognition scores of 44.4 ± 13.8 (maximum 56), 32.4 ± 5.1 (maximum 35), and 30.2 ± 6.0 (maximum 35), respectively. The results of the restricted cubic spline analysis reveal a clear positive linear correlation before school age (approximately 72 months), followed by a plateau (p for nonlinearity < 0.05). Traceable molecular data were available for thirteen participants, of whom nine (69%) had loss of methylation at chromosome 11p15 (11p15LOM), and four (31%) had maternal uniparental disomy of chromosome 7 (upd(7)mat). Of the 24 children, 46% required assistance with bathing, which was strongly correlated with self-care ability and body height. In contrast, most of the children had independence in mobility tasks such as walking and stair climbing. However, some required support in cognitive tasks, including problem-solving, comprehension, and expression. Overall, the included children reached a functional plateau later than the normative population, with the greatest delays in self-care and mobility domains. Conclusions: This study highlights that Taiwanese children with SRS require support in self-care and cognitive tasks. Functional independence in self-care and mobility domains was positively associated with body height. The WeeFIM questionnaire effectively identified strengths and limitations, emphasizing the need for individualized support in daily activities. Full article
(This article belongs to the Special Issue Advances in the Diagnosis and Management of Pediatric Diseases)
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29 pages, 12260 KB  
Article
Equilibrium Points and Periodic Orbits in the Circular Restricted Synchronous Three-Body Problem with Radiation and Mass Dipole Effects: Application to Asteroid 2001SN263
by Aguda Ekele Vincent, Jagadish Singh, George A. Tsirogiannis and Vassilis S. Kalantonis
Mathematics 2025, 13(7), 1150; https://doi.org/10.3390/math13071150 - 31 Mar 2025
Viewed by 592
Abstract
This study numerically explores the dynamics of the photogravitational circular restricted three-body problem, where an infinitesimal particle moves under the gravitational influence of two primary bodies connected by a massless rod. These primary masses revolve in circular orbits around their common center of [...] Read more.
This study numerically explores the dynamics of the photogravitational circular restricted three-body problem, where an infinitesimal particle moves under the gravitational influence of two primary bodies connected by a massless rod. These primary masses revolve in circular orbits around their common center of mass, which remains fixed at the origin of the coordinate system. The distance between the two masses remains constant, independent of their rotation period. The third body, being infinitesimally small compared to the primary masses, has a negligible effect on their motion. The primary mass is considered as a radiating body, while the secondary is modeled as an elongated one comprising two hypothetical point masses separated by a fixed distance. The analysis focuses on determining the number, location, and stability of equilibrium points, as well as examining the structure of zero-velocity curves under the influence of system parameters such as mass and force ratio, radiation pressure and geometric configuration of the secondary body. The system is found to allow up to six equilibria: four collinear and two non-collinear. Their number and positions are significantly affected by variations in the system’s parameters. Stability analysis reveals that the two non-collinear equilibrium points can exhibit stability under specific parameter configurations, while the four collinear points are typically unstable. An exception is the innermost collinear equilibrium point, which can be stable for certain parameter values. Our numerical investigation on periodic orbits around the collinear equilibrium points of the asteroid triple-system 2001SN263 show that a variation, either to the values of radiation or the force ratio parameters, influence their special characteristics such as period and stability. Also, their continuation in the space of initial conditions shows that all families terminate naturally at collision orbits with either the primary or the secondary. Full article
(This article belongs to the Section C2: Dynamical Systems)
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17 pages, 524 KB  
Article
Oral Administration of L-Arginine Improves the Growth and Survival of Sow-Reared Intrauterine Growth-Restricted Piglets
by David W. Long, Barry D. Long, Gayan I. Nawaratna and Guoyao Wu
Animals 2025, 15(4), 550; https://doi.org/10.3390/ani15040550 - 13 Feb 2025
Cited by 5 | Viewed by 1945
Abstract
Neonatal piglets with intrauterine growth restriction (IUGR) exhibit reduced rates of growth and survival. The present study tested the hypothesis that L-arginine supplementation can mitigate this problem. One hundred and twelve (112) IUGR piglets (with a mean birth weight of 0.84 kg) from [...] Read more.
Neonatal piglets with intrauterine growth restriction (IUGR) exhibit reduced rates of growth and survival. The present study tested the hypothesis that L-arginine supplementation can mitigate this problem. One hundred and twelve (112) IUGR piglets (with a mean birth weight of 0.84 kg) from 28 sows (four IUGR piglets/sow) were assigned randomly into one of four groups. Piglets were nursed by sows and orally administered 0, 0.1, 0.2, or 0.4 g L-arginine (in the form of L-arginine-HCl) per kg body weight (BW) twice daily between 0 and 14 days of age. The total doses of L-arginine were 0, 0.2, 0.4, or 0.8 g/kg BW/day. Appropriate amounts of L-alanine were added to L-arginine solutions so that all groups of piglets received the same amount of nitrogen. Piglets were weighed on days 0, 7, and 14 of age. On day 14, blood samples (5 mL) were obtained from the jugular vein of piglets at 1 h after suckling, and their milk consumption was measured over a 10-h period using the weigh–suckle–weigh technique. Milk intake did not differ (p > 0.05) among the four groups of piglets. Oral administration of 0.4 g L-arginine/kg BW/day increased (p < 0.05) the circulating levels of arginine, creatine, and anabolic hormones (insulin, growth hormone, and insulin-like growth factor-I), but decreased (p < 0.05) plasma concentrations of ammonia and cortisol (a catabolic hormone). Compared to the control group, IUGR piglets administered 0.2 and 0.4 g L-arginine/kg BW/day increased (p < 0.05) weight gain by 19% and 31%, respectively. Growth did not differ (p > 0.05) between the control and 0.8 g L-arginine/kg BW/day groups. The survival rates of IUGR piglets were 50%, 75%, 89%, and 89%, respectively, for the 0, 0.2, 0.4, and 0.8 g L-arginine/kg BW/day groups. Collectively, these results indicate that the growth and survival of IUGR piglets can be improved through L-arginine supplementation. Full article
(This article belongs to the Collection Comparative Animal Nutrition and Metabolism)
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15 pages, 23444 KB  
Article
Construction of the Red Swamp Crayfish (Procambarus clarkii) Family Selection Population and Whole Genome Sequencing to Screen WIPFI Candidate Genes Related to Growth
by Xing Tian, Xiudan Yuan, Zhigang He, Weiguo Li, Jinlong Li, Yong He, Shiming Deng, Jiarong Guo, Miaoquan Fang and Dongwu Wang
Genes 2025, 16(2), 174; https://doi.org/10.3390/genes16020174 - 31 Jan 2025
Cited by 1 | Viewed by 1396
Abstract
Background/Objectives: Procambarus clarkii is an important freshwater aquaculture species in China which has the characteristics of rich nutrition and delicious taste. However, the expansion of aquaculture scale, germplasm degradation, and other problems that have become increasingly prominent seriously restrict the sustainable development [...] Read more.
Background/Objectives: Procambarus clarkii is an important freshwater aquaculture species in China which has the characteristics of rich nutrition and delicious taste. However, the expansion of aquaculture scale, germplasm degradation, and other problems that have become increasingly prominent seriously restrict the sustainable development of the crayfish industry. Genetic improvement is an urgent need for the crayfish aquaculture industry, and selective breeding is an important way to improve the crayfish varieties. Methods: We established full-sibling family populations of the red swamp crayfish and performed whole-genome resequencing of the F3 family-selected red swamp crayfish population and wild red swamp crayfish populations from four regions of Hunan Province (Nanx, Mil, Caish, and Wangc). Results: The results showed that there was a clear separation between the wild population and the family population, and the decline rate was slightly faster in the wild population than that of the family breeding population. There was local gene flow between family populations, as well as gene flow between Mil, Caish, and families. In addition, 52 SNP loci related to body weight traits were identified by genome-wide association analysis, and the candidate gene WIPF1 related to growth was screened out. Conclusions: We established a line selection population of red swamp crayfish and obtained more stable candidate lines. In addition, this study identified Wiskott–Aldrich syndrome protein-interacting protein family member 1 (WIPF1) as a candidate gene related to body weight for the first time. The results provide a theoretical basis for exploring the growth mechanism of P. clarkii and carrying out in-depth genetic improvement. Full article
(This article belongs to the Special Issue Genetics and Genomics Applied to Aquatic Animal Science—2nd Edition)
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19 pages, 4141 KB  
Article
DNA Methylation Participates in Drought Stress Memory and Response to Drought in Medicago ruthenica
by Na Zi, Weibo Ren, Huiqin Guo, Feng Yuan, Yaling Liu and Ellen Fry
Genes 2024, 15(10), 1286; https://doi.org/10.3390/genes15101286 - 30 Sep 2024
Cited by 11 | Viewed by 2506
Abstract
Background: Drought is currently a global environmental problem, which inhibits plant growth and development and seriously restricts crop yields. Many plants exposed to drought stress can generate stress memory, which provides some advantages for resisting recurrent drought. DNA methylation is a mechanism [...] Read more.
Background: Drought is currently a global environmental problem, which inhibits plant growth and development and seriously restricts crop yields. Many plants exposed to drought stress can generate stress memory, which provides some advantages for resisting recurrent drought. DNA methylation is a mechanism involved in stress memory formation, and many plants can alter methylation levels to form stress memories; however, it remains unclear whether Medicago ruthenica exhibits drought stress memory, as the epigenetic molecular mechanisms underlying this process have not been described in this species. Methods: We conducted methylome and transcriptome sequencing to identify gene methylation and expression changes in plants with a history of two drought stress exposures. Results: Methylation analysis showed that drought stress resulted in an approximately 4.41% decrease in M. ruthenica genome methylation levels. The highest methylation levels were in CG dinucleotide contexts, followed by CHG contexts, with CHH contexts having the lowest levels. Analysis of associations between methylation and transcript levels showed that most DNA methylation was negatively correlated with gene expression except methylation within CHH motifs in gene promoter regions. Genes were divided into four categories according to the relationship between methylation and gene expression; the up-regulation of hypo-methylated gene expression accounted for the vast majority (692 genes) and included genes encoding factors key for abscisic acid (ABA) and proline synthesis. The hypo-methylation of the promoter and body regions of these two gene groups induced increased gene transcription levels. Conclusions: In conclusion, DNA methylation may contribute to drought stress memory formation and maintenance in M. ruthenica by increasing the transcription levels of genes key for ABA and proline biosynthesis. Full article
(This article belongs to the Section Genes & Environments)
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15 pages, 2285 KB  
Article
Effects of Methionine Restriction from Different Sources on Sperm Quality in Aging Mice
by Yinghui Wu, Hao Li, Yueyue Miao, Jian Peng and Hongkui Wei
Nutrients 2023, 15(22), 4782; https://doi.org/10.3390/nu15224782 - 15 Nov 2023
Cited by 4 | Viewed by 2155
Abstract
Decreased sperm quality causing poor pregnancy outcomes in aging males is a common problem. The aim of this study was to investigate the ameliorative effect of methionine restriction on sperm quality in aging mice, using methionine or 2-hydroxy-4-(methylthio)butanoate (HMTBA) as the methionine source, [...] Read more.
Decreased sperm quality causing poor pregnancy outcomes in aging males is a common problem. The aim of this study was to investigate the ameliorative effect of methionine restriction on sperm quality in aging mice, using methionine or 2-hydroxy-4-(methylthio)butanoate (HMTBA) as the methionine source, with a view to providing nutritional strategies to mitigate the decline in sperm quality in aging livestock. Fifty-one 6-week-old male mice were randomly divided into four groups: the non-aging group (NA, 0.86% methionine), the control diet group (CD, 0.86% methionine), the methionine-restricted group (MR, 0.17% methionine) and the HMTBA-restricted group (HR, 0.17% methionine). The mice in the CD, MR and HR groups were injected with a daily dose of 0.25 mL/20 g body weight of 10% D-galactose to establish an aging model. The test period was 42 days. The results showed that aging mice in the CD group had impaired testicular morphology and significantly decreased sperm quality compared to those in the NA group. Aging mice in the MR and HR groups showed attenuated impaired testicular morphology and improved sperm quality, especially sperm acrosomal integrity and membrane integrity, compared to mice in the CD group. In addition, mice in the MR and HR groups had reduced testicular inflammation and oxidative stress, increased spermidine levels, and reduced sperm RNA N6-methyladenosine (m6A) and DNA 5-methylcytosine (5mC) levels. Spermidine levels were positively correlated, whereas sperm RNA m6A and DNA 5mC levels were negatively correlated with sperm quality parameters. Our study suggests that methionine restriction alleviates the decline in sperm quality in aging mice, which may be related to changes in methionine metabolism and inhibition of sperm DNA and RNA methylation. Full article
(This article belongs to the Special Issue Protein, Amino Acids, and Healthspan)
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30 pages, 4164 KB  
Article
Analysis of Resonant Periodic Orbits in the Framework of the Perturbed Restricted Three Bodies Problem
by Bhavika M. Patel, Niraj M. Pathak and Elbaz I. Abouelmagd
Universe 2023, 9(5), 239; https://doi.org/10.3390/universe9050239 - 18 May 2023
Cited by 4 | Viewed by 1710
Abstract
In this work, the perturbed equations of motion of the infinitesimal body are constructed in the framework of the circular restricted three-body problem when the main two bodies are oblate and radiating. Under the perturbations effects of the oblateness and the radiation pressure [...] Read more.
In this work, the perturbed equations of motion of the infinitesimal body are constructed in the framework of the circular restricted three-body problem when the main two bodies are oblate and radiating. Under the perturbations effects of the oblateness and the radiation pressure the positions of collinear Lagrange points are evaluated, the interior and exterior first-order resonant periodic orbits are also studied. In addition, the initial positions of the periodic orbits and the size of loops have been estimated under these effects. Thus, the characteristics of periodic orbits have been studied under the combine effects of two, three and four perturbations for all the possible combinations of the perturbed parameters. The different order of resonant periodic orbits have been also analysed under the effects of Jacobi constant, mass factor, order of resonance and number of loops. Full article
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24 pages, 3383 KB  
Article
Geometric Analysis of Sun-Assisted Lunar Transfer Trajectories in the Planar Bicircular Four-Body Model
by Anastasia Tselousova, Sergey Trofimov, Maksim Shirobokov and Mikhail Ovchinnikov
Appl. Sci. 2023, 13(8), 4676; https://doi.org/10.3390/app13084676 - 7 Apr 2023
Cited by 6 | Viewed by 2060
Abstract
This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a [...] Read more.
This research presents a geometric analysis of Sun-assisted low-energy lunar transfers and several convenient tools that enable the systematic trajectory design in the framework of the planar bicircular restricted four-body problem. By analogy with the patched conic approximation approach for high-energy transfers, a Sun-assisted low-energy trajectory is divided into three legs. Two interior legs, departing and arriving, are located inside the Earth–Moon region of prevalence and designed in the Earth–Moon circular restricted three-body problem, whereas the exterior leg lies outside the region of prevalence and is calculated in the Earth–Moon–Sun bicircular restricted four-body model. The whole trajectory is obtained by smoothly patching the three legs on the boundary of the region of prevalence. The arrival conditions are met by targeting a specific point in the L2 lunar gateway. The interior legs are easily adjustable to the four-body dynamics. The database of planar lunar transfer trajectories can be used to select an initial guess for the multiple-shooting procedure of designing a three-dimensional Sun-assisted lunar transfer in high-fidelity dynamical models. Full article
(This article belongs to the Special Issue Advanced Schemes for Lunar Transfer, Descent and Landing)
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22 pages, 782 KB  
Article
A Study of Psychometric Instruments and Constructs of Work-Related Stress among Seafarers: A Qualitative Approach
by Siti Nazilah Mat Ali, Lucian-Ionel Cioca, Ruhiyah Sakinah Kayati, Jumadil Saputra, Muhammad Adam, Roxana Plesa and Raja Zirwatul Aida Raja Ibrahim
Int. J. Environ. Res. Public Health 2023, 20(4), 2866; https://doi.org/10.3390/ijerph20042866 - 6 Feb 2023
Cited by 10 | Viewed by 4005
Abstract
Due to unpredictable and demanding working circumstances and the significant potential for dangers and accidents, seafaring has been characterised as one of the world’s riskiest and stressful vocations that lead to physical and mental health problems. However, very few instruments measure work-related stress, [...] Read more.
Due to unpredictable and demanding working circumstances and the significant potential for dangers and accidents, seafaring has been characterised as one of the world’s riskiest and stressful vocations that lead to physical and mental health problems. However, very few instruments measure work-related stress, particularly in a seafaring context. None of the instruments are psychometrically sound. Therefore, a valid and reliable instrument to measure seafaring work-related stress is indispensable. This study aims to review work-related stress instruments and to explore the work-related stress construct among seafarers in Malaysia. This study uses a systematic review and semi-structured interviews across two phases. In Phase 1, we conducted a systematic review of several databases: Academic Search Ultimate, Emerald Journal Premier, Journal Storage (JSTOR), ScienceDirect, Springer Link, Taylor and Francis Online, and Wiley Online Library based on Preferred Reporting Items for Systematic Review and Meta-analyses (PRISMA). In 8975 articles, only 4 (four) studies used psychological instruments and 5 (five) studies used survey questionnaires to measure work-related stress. In Phase 2, we conducted a semi-structured interview with 25 (twenty-five) seafarers, online due to COVID-19 restrictions. The semi-structured interview indicated 6 (six) themes, namely, physical stress, personal issues, social living onboard, technostress, work factors, and the effect of the COVID-19 pandemic. In conclusion, the present study has identified three psychometric instruments for measuring work-related stress among seafarers: The Psychological General Well-Being Index, Perceived Stress Scale, and Job Content Questionnaire. We also found psychometric elements in some of the instruments are questionable, such as theoretical basis, construct development, and inadequate internal consistency value. In addition, this study also found that work-related stress is a multidimensional construct that needs to be studied based on work contexts. The findings of this study can contribute to the body of knowledge of a work-related stress construct in a seafaring context and could help to inform policy makers in the maritime industry. This study suggests a psychological instrument to measure work-related stress among seafarers in future studies. Full article
(This article belongs to the Special Issue 2nd Edition of Survey about Psychological Health)
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29 pages, 10962 KB  
Article
Design of a Low-Energy Earth-Moon Flight Trajectory Using a Planar Auxiliary Problem
by Ilya Nikolichev and Vladimir Sesyukalov
Appl. Sci. 2023, 13(3), 1967; https://doi.org/10.3390/app13031967 - 2 Feb 2023
Cited by 1 | Viewed by 1978
Abstract
The paper presents a sufficiently simple technique for designing a low-energy flight trajectory of a spacecraft (SC) from the Earth to the Moon with insertion into a low circular orbit of the latter. The proposed technique is based on the solution and subsequent [...] Read more.
The paper presents a sufficiently simple technique for designing a low-energy flight trajectory of a spacecraft (SC) from the Earth to the Moon with insertion into a low circular orbit of the latter. The proposed technique is based on the solution and subsequent analysis of a special model problem, which is a variant of the restricted circular four-body problem (RC4BP) Earth-Sun-SC-Moon; for which it is assumed that the planes of the orbits of all considered bodies coincides. The planar motion of the center of mass of the SC relative to the Earth is considered as perturbed (Sun, Moon). To describe it, equations in osculating elements are used, obtained by using the method of variation of constants based on the analytical solution of the planar circular restricted problem of two bodies (RC2BP)—Earth-SC, for which the rotation of the main axes of the coordinate system (the main plane) is synchronized with the motion of the Sun. The trajectory problem of designing a SC flight from a low circular near-Earth orbit to a low circular selenocentric one (“full” motion model—a restricted four-body problem (R4BP), an ephemeris model) is considered as an optimization one in the impulse formulation. The solution of the main problem is carried out in few (three) stages, on each the appropriate solution of the current variant of the auxiliary problem is determined, which is subsequently used as the basis of the initial approximation to the main one. Full article
(This article belongs to the Special Issue Advanced Schemes for Lunar Transfer, Descent and Landing)
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17 pages, 3427 KB  
Article
Semi-Analytical Approach in BiER4BP for Exploring the Stable Positioning of the Elements of a Dyson Sphere
by Sergey Ershkov, Dmytro Leshchenko and Evgeniy Yu. Prosviryakov
Symmetry 2023, 15(2), 326; https://doi.org/10.3390/sym15020326 - 24 Jan 2023
Cited by 7 | Viewed by 2801
Abstract
In this study, we present a new approach with semi-analytical and numerical findings for solving equations of motion of small orbiter m, which is moving under the combined gravitational attraction of three primaries, M1, M2, and M3 [...] Read more.
In this study, we present a new approach with semi-analytical and numerical findings for solving equations of motion of small orbiter m, which is moving under the combined gravitational attraction of three primaries, M1, M2, and M3, in case of the bi-elliptic restricted problem of four bodies (BiER4BP), where three such primaries, M1, M2, and M3, are moving on elliptic orbits with hierarchical configuration M3 << M2 << M1 within one plane as follows: third primary body M3 is moving on elliptical orbit around second M2, and second primary M2 is moving on elliptical orbit around first M1. Our aim for constructing the aforementioned quasi-planar motion of planetoid m is obtaining its coordinates supporting its orbit in a regime of close motion to the plane of orbiting the main bodies M1, M2, and M3. Meanwhile, the system of equations of motion was successfully numerically explored with respect to the existence and stable positioning of approximate solution for a Dyson sphere. As a result, the concept of the Dyson sphere for possible orbiting variety of solar energy absorbers was transformed to the elongated Dyson space net with respect to their trajectories for the successful process of absorbing the energy from the Sun; this can be recognized as symmetry reduction. We obtain the following: (1) the solution for coordinates {x, y} is described by the simplified system of two nonlinear ordinary differential equations of second order, depending on true anomaly f; (2) the expression for coordinate z is given by an equation of Riccati-type where small orbiter that quasi-oscillates close to the fixed plane {x,y,0}. Full article
(This article belongs to the Special Issue Symmetry in Fluid Dynamics)
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12 pages, 6764 KB  
Article
Study of Lagrange Points in the Earth–Moon System with Continuation Fractional Potential
by Lata Kumari Bairwa, Ashok Kumar Pal, Reena Kumari, Sawsan Alhowaity and Elbaz I. Abouelmagd
Fractal Fract. 2022, 6(6), 321; https://doi.org/10.3390/fractalfract6060321 - 8 Jun 2022
Cited by 10 | Viewed by 2605
Abstract
In this work, the restricted three-body system is studied in the framework of the continuation fractional potential with its application on the Earth–Moon system. With the help of a numerical technique, we obtained thirteen equilibrium points, such that nine of them are collinear [...] Read more.
In this work, the restricted three-body system is studied in the framework of the continuation fractional potential with its application on the Earth–Moon system. With the help of a numerical technique, we obtained thirteen equilibrium points, such that nine of them are collinear while the remaining four are non-collinear points. We found that the collinear points near the smaller primary were shifted outward from the Moon, whereas the points near the bigger primary were shifted towards the Earth as the value of the continuation fractional parameter increased. We analyzed the zero-velocity curves and discussed the perturbation of the continuation fractional potential effect on the possible regions of the motion. We also discussed the linear stability of all the equilibrium points and found that out of thirteen only two were stable. Due to such a prevalence, the continuation fractional potential is a source of significant perturbation, which embodies the lack of sphericity of the body in the restricted three-body problem Full article
(This article belongs to the Section General Mathematics, Analysis)
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21 pages, 6761 KB  
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 5 | Viewed by 3153
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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14 pages, 3401 KB  
Article
Probiotic Strains Isolated from an Olympic Woman’s Weightlifting Gold Medalist Increase Weight Loss and Exercise Performance in a Mouse Model
by Wen-Yang Lin, Yi-Wei Kuo, Jia-Hung Lin, Chi-Huei Lin, Jui-Fen Chen, Shin-Yu Tsai, Mon-Chien Lee, Yi-Ju Hsu, Chi-Chang Huang, Yung-An Tsou and Hsieh-Hsun Ho
Nutrients 2022, 14(6), 1270; https://doi.org/10.3390/nu14061270 - 17 Mar 2022
Cited by 6 | Viewed by 8836
Abstract
Obesity is a worldwide health problem. Calorie-restricted diets constitute a common intervention for treating obesity. However, an improper calorie-restricted diet can lead to malnutrition, fatigue, poor concretion, muscle loss, and reduced exercise performance. Probiotics have been introduced as an alternative treatment for obesity. [...] Read more.
Obesity is a worldwide health problem. Calorie-restricted diets constitute a common intervention for treating obesity. However, an improper calorie-restricted diet can lead to malnutrition, fatigue, poor concretion, muscle loss, and reduced exercise performance. Probiotics have been introduced as an alternative treatment for obesity. In the present study, we tested the weight loss and exercise performance enhancement effectiveness of probiotic strains of different origins, including four isolated from an Olympic weightlifting gold medalist (Bifidobacterium longum subsp. longum OLP-01, Lactobacillus plantarum PL-02, Lactobacillus salivarius subsp. salicinius SA-03, and Lactococcus lactis subsp. lactis LY-66). A high-fat diet (HFD) was used to induce obesity in 16 groups of mice (n = 8/group). The mice were administered probiotic supplements at a dosage of 4.1 × 109 CFU/kg/day for 10 weeks. All probiotic supplementation groups showed a significant reduction in body weight and fat mass compared with the HFD group. TYCA06, CS-773, BLI-02, PL-02, bv-77, and OLP-01 were the most effective in facilitating weight loss and fat reduction, which may be due to fatty-acid absorbing activity. PL-02, LY-66, TYCA06, CS-773, and OLP-01 elevated the animals’ grip strength and exhaustive running duration. PL-02, LY-66, and OLP-01 increased tissue glycogen (liver and muscle) levels and muscle capillary density and reduced blood lactate production levels after exercise. In conclusion, OLP-01, PL-02, LY-66, TYCA06, and CS-773 were highly effective in enhancing weight loss and exercise performance. This study should be repeated on humans in the future to further confirm the findings. Full article
(This article belongs to the Topic Probiotics, Prebiotics and Postbiotics in Human Health)
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