On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat

The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyro...

Full description

Saved in:
Bibliographic Details
Published in:Journal of applied and industrial mathematics 2023-09, Vol.17 (3), p.557-570
Main Authors: Kosov, A. A., Semenov, E. I.
Format: Article
Language:English
Subjects:
Equations of motion
Gyroscopic moment
Integrals
Mathematics
Mathematics and Statistics
Quadratures
Stability
Stability analysis
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites cdi_FETCH-LOGICAL-c1832-f848a4f43a3a9ef956fc3e3bbddf8a8752189c29f9cd9dbc08ca06c3aa2c42c83
container_end_page 570
container_issue 3
container_start_page 557
container_title Journal of applied and industrial mathematics
container_volume 17
creator Kosov, A. A.
Semenov, E. I.
description The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.
doi_str_mv 10.1134/S1990478923030092
format article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2886070034</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2886070034</sourcerecordid><originalsourceid>FETCH-LOGICAL-c1832-f848a4f43a3a9ef956fc3e3bbddf8a8752189c29f9cd9dbc08ca06c3aa2c42c83</originalsourceid><addsrcrecordid>eNp1kLtOwzAUhi0EEhX0AdgiMQdsHzexR1RBqVSpQ2AOjmO3gWIX20XKxjvwhjwJjsplQEznov87lx-hM4IvCAF2WREhMCu5oIABY0EP0Gho5awU5eFPzsUxGofQNRgILaAo6Ag9LG0W1zqb26hXXjbdpot9Jm2bVfG7cmYoYues9H1Wuc1uyMPQH9CZ871Ua_368fZeeR21DU99Nuu9C4k6RUdGboIef8UTdH9zfTe9zRfL2Xx6tcgV4UBzwxmXzDCQIIU2YlIYBRqapm0Nl7ycUMKFosII1Yq2UZgriQsFUlLFqOJwgs73c7fevex0iPWj23mbVtaU8wKXGANLKrJXqXRd8NrUW989p7dqguvBy_qPl4mheyYkrV1p_zv5f-gTuHt4Ww</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2886070034</pqid></control><display><type>article</type><title>On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat</title><source>Springer Link</source><creator>Kosov, A. A. ; Semenov, E. I.</creator><creatorcontrib>Kosov, A. A. ; Semenov, E. I.</creatorcontrib><description>The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.</description><identifier>ISSN: 1990-4789</identifier><identifier>EISSN: 1990-4797</identifier><identifier>DOI: 10.1134/S1990478923030092</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Equations of motion ; Gyroscopic moment ; Integrals ; Mathematics ; Mathematics and Statistics ; Quadratures ; Stability ; Stability analysis</subject><ispartof>Journal of applied and industrial mathematics, 2023-09, Vol.17 (3), p.557-570</ispartof><rights>Pleiades Publishing, Ltd. 2023</rights><rights>Pleiades Publishing, Ltd. 2023.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c1832-f848a4f43a3a9ef956fc3e3bbddf8a8752189c29f9cd9dbc08ca06c3aa2c42c83</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kosov, A. A.</creatorcontrib><creatorcontrib>Semenov, E. I.</creatorcontrib><title>On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat</title><title>Journal of applied and industrial mathematics</title><addtitle>J. Appl. Ind. Math</addtitle><description>The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.</description><subject>Equations of motion</subject><subject>Gyroscopic moment</subject><subject>Integrals</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Quadratures</subject><subject>Stability</subject><subject>Stability analysis</subject><issn>1990-4789</issn><issn>1990-4797</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp1kLtOwzAUhi0EEhX0AdgiMQdsHzexR1RBqVSpQ2AOjmO3gWIX20XKxjvwhjwJjsplQEznov87lx-hM4IvCAF2WREhMCu5oIABY0EP0Gho5awU5eFPzsUxGofQNRgILaAo6Ag9LG0W1zqb26hXXjbdpot9Jm2bVfG7cmYoYues9H1Wuc1uyMPQH9CZ871Ua_368fZeeR21DU99Nuu9C4k6RUdGboIef8UTdH9zfTe9zRfL2Xx6tcgV4UBzwxmXzDCQIIU2YlIYBRqapm0Nl7ycUMKFosII1Yq2UZgriQsFUlLFqOJwgs73c7fevex0iPWj23mbVtaU8wKXGANLKrJXqXRd8NrUW989p7dqguvBy_qPl4mheyYkrV1p_zv5f-gTuHt4Ww</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Kosov, A. A.</creator><creator>Semenov, E. I.</creator><general>Pleiades Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope></search><sort><creationdate>20230901</creationdate><title>On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat</title><author>Kosov, A. A. ; Semenov, E. I.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1832-f848a4f43a3a9ef956fc3e3bbddf8a8752189c29f9cd9dbc08ca06c3aa2c42c83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Equations of motion</topic><topic>Gyroscopic moment</topic><topic>Integrals</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Quadratures</topic><topic>Stability</topic><topic>Stability analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kosov, A. A.</creatorcontrib><creatorcontrib>Semenov, E. I.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical &amp; Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of applied and industrial mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kosov, A. A.</au><au>Semenov, E. I.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat</atitle><jtitle>Journal of applied and industrial mathematics</jtitle><stitle>J. Appl. Ind. Math</stitle><date>2023-09-01</date><risdate>2023</risdate><volume>17</volume><issue>3</issue><spage>557</spage><epage>570</epage><pages>557-570</pages><issn>1990-4789</issn><eissn>1990-4797</eissn><abstract>The equations of motion of the Goryachev–Sretensky gyrostat are studied. All stationary solutions are found on the invariant set of the zero level of the area integral, and their stability is analyzed. For the case where the suspension point coincides with the center of mass and the action of a gyroscopic moment is of a special type, integration by quadratures is performed.</abstract><cop>Moscow</cop><pub>Pleiades Publishing</pub><doi>10.1134/S1990478923030092</doi><tpages>14</tpages></addata></record>
fulltext fulltext
identifier ISSN: 1990-4789
ispartof Journal of applied and industrial mathematics, 2023-09, Vol.17 (3), p.557-570
issn 1990-4789
1990-4797
language eng
recordid cdi_proquest_journals_2886070034
source Springer Link
subjects Equations of motion
Gyroscopic moment
Integrals
Mathematics
Mathematics and Statistics
Quadratures
Stability
Stability analysis
title On the Integrability and Stability of Stationary Solutions of the Goryachev–Sretensky Gyrostat
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T05%3A48%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Integrability%20and%20Stability%20of%20Stationary%20Solutions%20of%20the%20Goryachev%E2%80%93Sretensky%20Gyrostat&rft.jtitle=Journal%20of%20applied%20and%20industrial%20mathematics&rft.au=Kosov,%20A.%20A.&rft.date=2023-09-01&rft.volume=17&rft.issue=3&rft.spage=557&rft.epage=570&rft.pages=557-570&rft.issn=1990-4789&rft.eissn=1990-4797&rft_id=info:doi/10.1134/S1990478923030092&rft_dat=%3Cproquest_cross%3E2886070034%3C/proquest_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c1832-f848a4f43a3a9ef956fc3e3bbddf8a8752189c29f9cd9dbc08ca06c3aa2c42c83%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2886070034&rft_id=info:pmid/&rfr_iscdi=true