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Efficient Techniques to Cope with Chaotic Dynamics in Deterministic Systems
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S0038094624601828
Pablo M. Cincotta,  Claudia M. Giordano
{"title":"Efficient Techniques to Cope with Chaotic Dynamics in Deterministic Systems","authors":"Pablo M. Cincotta,&nbsp; Claudia M. Giordano","doi":"10.1134/S0038094624601828","DOIUrl":"10.1134/S0038094624601828","url":null,"abstract":"<p>In this work we review and improve two useful techniques to cope with chaotic dynamics in deterministic systems, namely the Mean Exponential Growth factor of Nearby Orbits (MEGNO) and the Shannon entropy. The MEGNO provides a direct measure of the hyperbolic dynamics in an arbitrary small neighborhood of a given point of the phase space in comparatively short motion times and the maximum Lyapunov exponent (or its spectrum) can be easily derived from this fast dynamical indicator which has become a wide-spread tool in the investigation of the global dynamics in planetary systems. The time derivative of the Shannon entropy yields a confident measure of the diffusion speed in comparison with the usual approach of the action-like variance evolution. It has been successfully applied in different dynamical systems, particularly, in exoplanetary systems. A brief discussion concerning the relationship among the Shannon entropy and the Kolmogorov–Sinai or metric entropy and the topological entropy is also addressed. Both methods allow to get two relevant timescales in chaotic dynamics, the Lyapunov time and the diffusion time. An application to a simple 4D symplectic map illustrates the efficiency of both techniques.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algorithms for Computing Hamiltonian Normal Form
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S0038094624601853
A. G. Petrov, A. B. Batkhin
{"title":"Algorithms for Computing Hamiltonian Normal Form","authors":"A. G. Petrov,&nbsp;A. B. Batkhin","doi":"10.1134/S0038094624601853","DOIUrl":"10.1134/S0038094624601853","url":null,"abstract":"<p>The invariant normalization method proposed by V.F. Zhuravlev, used for calculating normal or symmetrized forms of autonomous Hamiltonian systems, is discussed. The normalizing canonical transformation is represented by a Lie series using a generating Hamiltonian. This method has a generalization proposed by A.G. Petrov, which normalizes not only autonomous but also nonautonomous Hamiltonian systems. The normalizing canonical transformation is represented by a series using a parametric function. For autonomous Hamiltonian systems, the first two approximation steps in both methods are the same, and the remaining steps are different. The normal forms of both methods are identical. A method for testing a normalization program has also been proposed. For this purpose, the Hamiltonian of a strongly nonlinear Hamiltonian system is found, for which the normal form is a quadratic Hamiltonian. The normalizing transformation is expressed in terms of elementary functions.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Calculation of Precession of Space Objects Using an Approximate Theory of a Gyroscope with Error Estimation
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S0038094624601816
A. G. Petrov
{"title":"Calculation of Precession of Space Objects Using an Approximate Theory of a Gyroscope with Error Estimation","authors":"A. G. Petrov","doi":"10.1134/S0038094624601816","DOIUrl":"10.1134/S0038094624601816","url":null,"abstract":"<p>A space object is considered as a dynamically symmetric rigid body with a fixed point at the center of mass under the action of a periodic moment of force. Two small parameters are introduced: the first characterizes the smallness of the amplitude of the moment of force, and the second characterizes the smallness of the component of the kinetic moment perpendicular to the axis of symmetry. The smallness of the second parameter is usually the basis for using the approximate theory of the gyroscope. Using this approximation, one can quite easily find the speed of precession of the top under the action of a small periodic torque. It is shown that the relative error of the precession period calculated in this way is very small: it is proportional to the product of two small parameters. In this way, a simple formula is found for the precession of the Earth’s satellite under the influence of the Earth’s gravitational field. The resulting formula for the speed of the lunar–solar precession of the Earth agrees well with astronomical observations.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Three-Body Problem in Shape Space
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S0038094624601877
V. B. Titov
{"title":"The Three-Body Problem in Shape Space","authors":"V. B. Titov","doi":"10.1134/S0038094624601877","DOIUrl":"10.1134/S0038094624601877","url":null,"abstract":"<p>The general three-body problem is considered in shape space. Solutions to the problem in such a space have a number of remarkable properties. The paper presents the equations of motion of the three-body problem in shape space, the integrals of the problem are investigated. As it turns out, Sundman’s inequality is a simple consequence of the energy integral in the shape space. The periodic solutions obtained of the three-body problem are considered in shape space, and their properties are studied.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
4D Modeling of Kinematics of a Selected Galaxy Subsystem
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S0038094624601786
I. I. Nikiforov
{"title":"4D Modeling of Kinematics of a Selected Galaxy Subsystem","authors":"I. I. Nikiforov","doi":"10.1134/S0038094624601786","DOIUrl":"10.1134/S0038094624601786","url":null,"abstract":"<p><b>Abstract</b>—A four-dimensional method of optimization of spatial-kinematic models of subsystems of objects of the Galaxy based on the principle of maximum likelihood has been proposed, taking into account the measurement and natural (dynamic) uncertainty of 3D velocities and random errors of heliocentric distances (in this case, trigonometric parallaxes). The method has been tested on masers in the high-mass star-forming regions (HMSFRs). Based on the data on these objects, new estimates of the fundamental parameters of the Galaxy were obtained, free from systematic biases due to parallax errors, in particular, the distance from the Sun to the center of the Galaxy <i>R</i><sub>0</sub> = 7.88 ± 0.12 kpc, the angular azimuthal velocity of the Sun <span>({{omega }_{ odot }})</span> = 30.40 ± 0.20 km/s/kpc, the linear azimuthal velocity of the Sun <span>({{theta }_{ odot }})</span> = 239.6 ± 4.0 km/s/kpc.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Numerical and Analytical Approach to the Study of Resonant Structures of Near-Planetary Orbital Spaces
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-14 DOI: 10.1134/S003809462460183X
I. V. Tomilova, T. V. Bordovitsyna, A. G. Aleksandrova, E. V. Blinkova, N. A. Popandopulo, T. V. Shaforostov
{"title":"Numerical and Analytical Approach to the Study of Resonant Structures of Near-Planetary Orbital Spaces","authors":"I. V. Tomilova,&nbsp;T. V. Bordovitsyna,&nbsp;A. G. Aleksandrova,&nbsp;E. V. Blinkova,&nbsp;N. A. Popandopulo,&nbsp;T. V. Shaforostov","doi":"10.1134/S003809462460183X","DOIUrl":"10.1134/S003809462460183X","url":null,"abstract":"<p>In this paper, the authors summarize eight years of experience in the development and application of a numerical-analytical method for studying resonant structures in near-Earth and near-lunar space. The dynamics of near-Earth objects are considered in the following: orbital (tesseral) resonances of the second to tenth orders, secular apsidal-nodal resonances of the second to sixth orders, semisecular resonances with the average motion of the third body of the second to fifth orders, as well as secondary resonances arising under the influence of light pressure. In the dynamics of lunar objects, manifestations of secular and semisecular resonances are considered, and an analysis of the dynamics of low-flying objects is given.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analytical Methods of Celestial Mechanics—2024
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-13 DOI: 10.1134/S0038094624601889
N. N. Vasiliev, I. I. Shevchenko, V. B. Titov
{"title":"Analytical Methods of Celestial Mechanics—2024","authors":"N. N. Vasiliev,&nbsp;I. I. Shevchenko,&nbsp;V. B. Titov","doi":"10.1134/S0038094624601889","DOIUrl":"10.1134/S0038094624601889","url":null,"abstract":"","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Influence of Asteroid Shape Deformations When Approaching the Earth on Rotational State Disturbances and the Value of the Yarkovsky Effect
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-13 DOI: 10.1134/S0038094624601774
A. V. Melnikov, K. S. Lobanova
{"title":"Influence of Asteroid Shape Deformations When Approaching the Earth on Rotational State Disturbances and the Value of the Yarkovsky Effect","authors":"A. V. Melnikov,&nbsp;K. S. Lobanova","doi":"10.1134/S0038094624601774","DOIUrl":"10.1134/S0038094624601774","url":null,"abstract":"<p>Using numerical experiments, an analysis was made of the influence of changes in the shape of the asteroid on the magnitude of disturbances occurring in its rotational motion during close approach to the Earth. The influence of perturbations in the rotation of an asteroid (changes in the period and orientation of the rotation axis) on the orbital dynamics is considered by changing the magnitude of the Yarkovsky effect. It has been established that during tidal deformation of the asteroid’s figure due to its approach to the Earth, accompanied by a change in the moments of inertia, the magnitude of the perturbations in rotation is significantly higher than in the case of an unchanged figure. It has been shown that a 10–25% change in the inertial parameters of the asteroid (99 942) Apophis during its approach to the Earth in 2029 leads to a 2–4-fold increase in the size of the regions in which the rotation period and the angle characterizing the inclination of the rotation axis to the orbital plane can change. Perturbations in the rotation of the asteroid lead to a change in the parameter <i>A</i><sub>2</sub>, characterizing the Yarkovsky effect. The size of the region of change of parameter <i>A</i><sub>2</sub> in the presence of deformations in the asteroid’s figure also increases significantly compared to the case of an unchanged figure.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Lunar Ephemeris Parameters for the EPM2023a
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-13 DOI: 10.1134/S0038094624601798
M. A. Lebedeva, E. I. Yagudina
{"title":"Lunar Ephemeris Parameters for the EPM2023a","authors":"M. A. Lebedeva,&nbsp;E. I. Yagudina","doi":"10.1134/S0038094624601798","DOIUrl":"10.1134/S0038094624601798","url":null,"abstract":"<p>Since 1969, the Lunar Laser Ranging (LLR) technique has been used to build and improve the ephemeris of the Moon. The results of processing of new laser observations are considered here to determine more accurately the lunar ephemeris parameters for the Ephemeris of Planets and the Moon (version EPM2023a), which was created and is maintained by the Institute of Applied Astronomy of the Russian Academy of Sciences. In 2014, the development of a new version of the EPM (including the Moon) started within the upgraded ERA-8 system (where ERA stands for Ephemeris Research in Astronomy). The new version of the lunar ephemeris implements a model of the orbital–rotational motion of the Moon that is similar to that used in the DE430 version of the NASA JPL Development Ephemerides. In this model, the Moon is considered as an elastic body with a rotating liquid core, and the rotation of the Moon around its center of mass in the celestial coordinate system is described by three Euler angles. Together with new geophysical and geodynamic parameters required today, this model replaced the model proposed by G.A. Krasinsky in the ERA-7 system. In this paper, to obtain the lunar ephemeris parameters for the EPM2023a, we use 33 602 Lunar Laser Ranging observations (LLRos; i.e., normal points), including 1985 new observations. About 100 lunar ephemeris parameters of the EPM2023a were improved, and some of them were compared to the corresponding parameters of the INPOP21a (where INPOP stands for Integration Numerique Planetaire de l’Observatoire de Paris) and DE440 ephemerides. For current projects and practical work in space research, it is necessary to use the latest lunar ephemerides—EPM2022a and EPM2023a.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Resonant Outcomes of Interactions of Massive Interstellar Objects with the Solar System
IF 0.6 4区 物理与天体物理
Solar System Research Pub Date : 2025-05-13 DOI: 10.1134/S0038094624601907
D. V. Mikryukov, I. I. Shevchenko
{"title":"Resonant Outcomes of Interactions of Massive Interstellar Objects with the Solar System","authors":"D. V. Mikryukov,&nbsp;I. I. Shevchenko","doi":"10.1134/S0038094624601907","DOIUrl":"10.1134/S0038094624601907","url":null,"abstract":"<p>The paper studies the consequences of probable encounters of interstellar objects of planetary mass (free-floating exoplanets) with the Solar System. As a result of such approaches, mean motion resonances may arise in the dynamics of planets, but entering into the resonances is possible only with selected values of the mass of the interstellar object and the initial conditions of its motion. The most significant resonances that can arise as a result of the approaches have been identified.</p>","PeriodicalId":778,"journal":{"name":"Solar System Research","volume":"59 4","pages":""},"PeriodicalIF":0.6,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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