The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Trajectory and stability of Lagrangian point L2L_2 in the Sun-Earth system

This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the model for the Sun-Earth system. The effect of radiation pressure of the Sun and oblate shape of the Earth are considered. The point $L_2$ is asymptotically stable upto a specific value of time $t$ correspond to each set of values of parameters and initial conditions. The results obtained from this study would be applicable to locate a satellite, a telescope or a space station around the point $L_2$.Comment: Accepted for publication in Astrophysics & Space Scienc

Modern pedagogical technologies in the system of additional professional education

The text of this article reflects the results of theoretical and practical research in the field of equipping the system of additional professional education with the means of modern pedagogical technologies that affect the quality of professional training of future specialists. The most relevant pedagogical technologies are considered separately, and their effectiveness or ineffectiveness is confirmed by means of online questionnaires. Besides, a significant segment of the study is devoted to reviewing and comparing the experience of predecessors in this matter. The role of personality –oriented and competence-based approaches in the system of additional vocational education is revealed and actualized, their individual elements, especially significant for research, are singled out. A special place in the structure of the study is occupied by the chosen key method – online questionnaire, which is based on data provided by more than 150 teachers of the systems of both higher professional and additional professional education. All of them are not geographically tied to one place, in connection with which one can judge the objectivity of their opinions, as well as the vast geography of the dissemination of the research results. This method is one of the most effective and promising methods of scientific analytical and reflective research

Правозащитная деятельность Льва Николаевича Толстого

Russian jurisprudence has a long history of development, in which individuals played an important role: lawyers, human rights defenders, counsels. Leo Nikolayevich Tolstoy is known not only as a famous writer, but also as a public figure, who made a significant contribution to the development of original political and legal ideas about law, the system of public administration, international relations, education and other important areas of life. The article is devoted to the study of the legal thought of the writer. The authors analyze the public legal activity of Leo Nikolayevich and his role in the development of domestic jurisprudence.Российская юриспруденция имеет длительную историю развития в которой немаловажную роль сыграли отдельные личности: юристы, правозащитники, адвокаты. Лев Николаевич Толстой известен не только как знаменитый писатель, но и общественный деятель, внесший существенный вклад в разработку оригинальных политико-правовых представлений о праве, системе государственного управления, международных отношений, образования и других важных сфер жизни. Статья посвящена изучению правовой мысли писателя. Авторами анализируется общественная правовая деятельность Льва Николаевича и его роль в развитии отечественной юриспруденции

Human rights activities of Leo Tolstoy

Russian jurisprudence has a long history of development, in which individuals played an important role: lawyers, human rights defenders, counsels. Leo Nikolayevich Tolstoy is known not only as a famous writer, but also as a public figure, who made a significant contribution to the development of original political and legal ideas about law, the system of public administration, international relations, education and other important areas of life. The article is devoted to the study of the legal thought of the writer. The authors analyze the public legal activity of Leo Nikolayevich and his role in the development of domestic jurisprudence. © 2019 Rossiiskaya Akademiya Nauk, Institut Istorii Russian Academy of Sciences, Institute of General Hist. All rights reserved