<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE root>
<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" article-type="research-article" dtd-version="1.2" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">Доклады Академии наук</journal-id><journal-title-group><journal-title xml:lang="en">Доклады Академии наук</journal-title><trans-title-group xml:lang="ru"><trans-title>Доклады Академии наук</trans-title></trans-title-group></journal-title-group><issn publication-format="print">0869-5652</issn><publisher><publisher-name xml:lang="en">The Russian Academy of Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">17929</article-id><article-id pub-id-type="doi">10.31857/S0869-56524892147-151</article-id><article-categories><subj-group subj-group-type="toc-heading" xml:lang="en"><subject>Mechanics</subject></subj-group><subj-group subj-group-type="toc-heading" xml:lang="ru"><subject>Механика</subject></subj-group><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group></article-categories><title-group><article-title xml:lang="en">The implementation of a given motion of a rigid body relative to its center of mass by moving the material point</article-title><trans-title-group xml:lang="ru"><trans-title>Осуществление заданного движения твёрдого тела относительно своего центра масс перемещением материальной точки</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author"><name-alternatives><name xml:lang="en"><surname>Shmatkov</surname><given-names>A. M.</given-names></name><name xml:lang="ru"><surname>Шматков</surname><given-names>А. М.</given-names></name></name-alternatives><address><country country="RU">Russian Federation</country></address><email>shmatkov@ipmnet.ru</email><xref ref-type="aff" rid="aff1"/></contrib></contrib-group><aff-alternatives id="aff1"><aff><institution xml:lang="en">Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences</institution></aff><aff><institution xml:lang="ru">Институт проблем механики имени А.Ю. Ишлинского Российской академии наук</institution></aff></aff-alternatives><pub-date date-type="pub" iso-8601-date="2019-11-20" publication-format="electronic"><day>20</day><month>11</month><year>2019</year></pub-date><volume>489</volume><issue>2</issue><issue-title xml:lang="en"/><issue-title xml:lang="ru"/><fpage>147</fpage><lpage>151</lpage><history><date date-type="received" iso-8601-date="2019-11-30"><day>30</day><month>11</month><year>2019</year></date><date date-type="accepted" iso-8601-date="2019-11-30"><day>30</day><month>11</month><year>2019</year></date></history><permissions><copyright-statement xml:lang="en">Copyright ©; 2019, Russian academy of sciences</copyright-statement><copyright-statement xml:lang="ru">Copyright ©; 2019, Российская академия наук</copyright-statement><copyright-year>2019</copyright-year><copyright-holder xml:lang="en">Russian academy of sciences</copyright-holder><copyright-holder xml:lang="ru">Российская академия наук</copyright-holder></permissions><self-uri xlink:href="https://journals.eco-vector.com/0869-5652/article/view/17929">https://journals.eco-vector.com/0869-5652/article/view/17929</self-uri><abstract xml:lang="en"><p>In the absence of external forces for a mechanical system consisting of an interacting solid body and a material point, a law of movement of a point is constructed that realizes a given body motion in the Koenig coordinate system. Conditions found that this movement has to satisfy. The result can be used both to create capsule robots and to control spacecraft. An example of applying the obtained formula is given.</p></abstract><trans-abstract xml:lang="ru"><p>При отсутствии внешних сил для механической системы, состоящей из взаимодействующих твёрдого тела и материальной точки, построен закон перемещения точки, реализующий заданное движение тела в системе координат Кёнига. Найдены условия, которым должно удовлетворять это движение. Результат может быть использован как при создании капсульных роботов, так и при управлении космическими аппаратами. Приведён пример применения полученной формулы.</p></trans-abstract><kwd-group xml:lang="en"><kwd>control using the moving mass</kwd><kwd>Koenig axes</kwd><kwd>realization of the given movement</kwd></kwd-group><kwd-group xml:lang="ru"><kwd>управление с помощью подвижной массы</kwd><kwd>оси Кёнига</kwd><kwd>осуществление заданного движения</kwd></kwd-group><funding-group><funding-statement xml:lang="en">This work was supported by the Russian Science Foundation (grant 18-11-00307).</funding-statement><funding-statement xml:lang="ru">Работа выполнена при финансовой поддержке Российского научного фонда (грант 18-11-00307).</funding-statement></funding-group></article-meta></front><body></body><back><ref-list><ref id="B1"><label>1.</label><mixed-citation>Schmoeckel F., Worn H. Remotely Controllable Microrobots Acting as Nano Positioners and Intelligent Tweezers in Scanning Electron Microscopes (SEMs) // Proc. Intern. Conf. Robotics and Automation. IEEE. N.Y., 2001. V. 4. P. 3903-3913.</mixed-citation></ref><ref id="B2"><label>2.</label><mixed-citation>Vartholomeos P., Papadopoulos E. Dynamics, Design and Simulation of a Novel Microrobotic Platform Employing Vibration Microactuators // Transactions of ASME. J. Dynamical Systems, Measurement and Control. 2006. V. 128. P. 122-133.</mixed-citation></ref><ref id="B3"><label>3.</label><mixed-citation>Chernousko F. L. Two-Dimensional Motions of a Body Containing Internal Moving Masses // Meccanica. 2016. V. 51. № 12. P. 3203-3209.</mixed-citation></ref><ref id="B4"><label>4.</label><mixed-citation>Маркеев А. П. Теоретическая механика. М.: ЧеРо, 1999. 572 с.</mixed-citation></ref><ref id="B5"><label>5.</label><mixed-citation>Черноусько Ф. Л. Управление ориентацией твердого тела с помощью внутренней массы // Прикладная механика и техн. физика. 2019. № 2. C. 107-112.</mixed-citation></ref><ref id="B6"><label>6.</label><mixed-citation>Журавлев В. Ф. Основы теоретической механики. М.: Физматлит, 2008. 304 с.</mixed-citation></ref><ref id="B7"><label>7.</label><mixed-citation>Рашевский П. К. Курс дифференциальной геометрии. М.; Л.: ГИТТЛ, 1950. 428 с.</mixed-citation></ref></ref-list></back></article>
