The inhomogeneous Suslov problem
We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case...
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| Veröffentlicht in: | Physics letters. A 2014-06, Vol.378 (32-33), p.2389-2394 |
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| container_issue | 32-33 |
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| container_title | Physics letters. A |
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| creator | García-Naranjo, Luis C. Maciejewski, Andrzej J. Marrero, Juan C. Przybylska, Maria |
| description | We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case, possess a smooth invariant measure. Interestingly, in this generic case, the first integral that permits integration is transcendental and the density of the invariant measure depends on the angular velocities. We also study the Painlevé property of the solutions.
•We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints.•We study the problem in detail for a particular choice of the parameters that has a clear physical interpretation.•We show that the equations of motion possess an invariant measure whose density depends on the velocity variables.•We show that the reduced system is integrable due to the existence of a transcendental first integral.•We study the Painlevé property of the solutions. |
| doi_str_mv | 10.1016/j.physleta.2014.06.026 |
| format | Article |
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•We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints.•We study the problem in detail for a particular choice of the parameters that has a clear physical interpretation.•We show that the equations of motion possess an invariant measure whose density depends on the velocity variables.•We show that the reduced system is integrable due to the existence of a transcendental first integral.•We study the Painlevé property of the solutions.</description><identifier>ISSN: 0375-9601</identifier><identifier>EISSN: 1873-2429</identifier><identifier>DOI: 10.1016/j.physleta.2014.06.026</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Angular velocity ; Density ; Inertia ; Integrability ; Integrals ; Invariant volume forms ; Invariants ; Mathematical analysis ; Nonholonomic mechanical systems ; Rigid-body dynamics ; Solid state physics ; Suslov problem</subject><ispartof>Physics letters. A, 2014-06, Vol.378 (32-33), p.2389-2394</ispartof><rights>2014 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c463t-1d52647f67c428d46bee17a47ea27ea8d3e709b0bd3ab7c26434d47133e2f40c3</citedby><cites>FETCH-LOGICAL-c463t-1d52647f67c428d46bee17a47ea27ea8d3e709b0bd3ab7c26434d47133e2f40c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0375960114005957$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids></links><search><creatorcontrib>García-Naranjo, Luis C.</creatorcontrib><creatorcontrib>Maciejewski, Andrzej J.</creatorcontrib><creatorcontrib>Marrero, Juan C.</creatorcontrib><creatorcontrib>Przybylska, Maria</creatorcontrib><title>The inhomogeneous Suslov problem</title><title>Physics letters. A</title><description>We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case, possess a smooth invariant measure. Interestingly, in this generic case, the first integral that permits integration is transcendental and the density of the invariant measure depends on the angular velocities. We also study the Painlevé property of the solutions.
•We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints.•We study the problem in detail for a particular choice of the parameters that has a clear physical interpretation.•We show that the equations of motion possess an invariant measure whose density depends on the velocity variables.•We show that the reduced system is integrable due to the existence of a transcendental first integral.•We study the Painlevé property of the solutions.</description><subject>Angular velocity</subject><subject>Density</subject><subject>Inertia</subject><subject>Integrability</subject><subject>Integrals</subject><subject>Invariant volume forms</subject><subject>Invariants</subject><subject>Mathematical analysis</subject><subject>Nonholonomic mechanical systems</subject><subject>Rigid-body dynamics</subject><subject>Solid state physics</subject><subject>Suslov problem</subject><issn>0375-9601</issn><issn>1873-2429</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNqFkM1OwzAQhC0EEqXwCihHLgnrn9rNDVRBQarEgXK2HHtDXSV1sdNKfXtcCmcOq73MzO58hNxSqChQeb-utqtD6nAwFQMqKpAVMHlGRnSqeMkEq8_JCLialLUEekmuUloDZCfUI1IsV1j4zSr04RM3GHapeN-lLuyLbQxNh_01uWhNl_Dmd4_Jx_PTcvZSLt7mr7PHRWmF5ENJ3YRJoVqprGBTJ2SDSJURCg3LM3UcFdQNNI6bRtms5cIJRTlH1gqwfEzuTrn57tcO06B7nyx2nfn5SlOpqKRqkjuNiTxJbQwpRWz1NvrexIOmoI9I9Fr_IdFHJBqkzkiy8eFkxFxk7zHqZD1uLDof0Q7aBf9fxDfc4GzO</recordid><startdate>20140627</startdate><enddate>20140627</enddate><creator>García-Naranjo, Luis C.</creator><creator>Maciejewski, Andrzej J.</creator><creator>Marrero, Juan C.</creator><creator>Przybylska, Maria</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7QQ</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope></search><sort><creationdate>20140627</creationdate><title>The inhomogeneous Suslov problem</title><author>García-Naranjo, Luis C. ; Maciejewski, Andrzej J. ; Marrero, Juan C. ; Przybylska, Maria</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463t-1d52647f67c428d46bee17a47ea27ea8d3e709b0bd3ab7c26434d47133e2f40c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Angular velocity</topic><topic>Density</topic><topic>Inertia</topic><topic>Integrability</topic><topic>Integrals</topic><topic>Invariant volume forms</topic><topic>Invariants</topic><topic>Mathematical analysis</topic><topic>Nonholonomic mechanical systems</topic><topic>Rigid-body dynamics</topic><topic>Solid state physics</topic><topic>Suslov problem</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>García-Naranjo, Luis C.</creatorcontrib><creatorcontrib>Maciejewski, Andrzej J.</creatorcontrib><creatorcontrib>Marrero, Juan C.</creatorcontrib><creatorcontrib>Przybylska, Maria</creatorcontrib><collection>CrossRef</collection><collection>Ceramic Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physics letters. A</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>García-Naranjo, Luis C.</au><au>Maciejewski, Andrzej J.</au><au>Marrero, Juan C.</au><au>Przybylska, Maria</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The inhomogeneous Suslov problem</atitle><jtitle>Physics letters. A</jtitle><date>2014-06-27</date><risdate>2014</risdate><volume>378</volume><issue>32-33</issue><spage>2389</spage><epage>2394</epage><pages>2389-2394</pages><issn>0375-9601</issn><eissn>1873-2429</eissn><abstract>We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints. We show that if the direction along which the Suslov constraint is enforced is perpendicular to a principal axis of inertia of the body, then the reduced equations are integrable and, in the generic case, possess a smooth invariant measure. Interestingly, in this generic case, the first integral that permits integration is transcendental and the density of the invariant measure depends on the angular velocities. We also study the Painlevé property of the solutions.
•We consider the Suslov problem of nonholonomic rigid body motion with inhomogeneous constraints.•We study the problem in detail for a particular choice of the parameters that has a clear physical interpretation.•We show that the equations of motion possess an invariant measure whose density depends on the velocity variables.•We show that the reduced system is integrable due to the existence of a transcendental first integral.•We study the Painlevé property of the solutions.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.physleta.2014.06.026</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Physics letters. A, 2014-06, Vol.378 (32-33), p.2389-2394 |
| issn | 0375-9601 1873-2429 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Angular velocity Density Inertia Integrability Integrals Invariant volume forms Invariants Mathematical analysis Nonholonomic mechanical systems Rigid-body dynamics Solid state physics Suslov problem |
| title | The inhomogeneous Suslov problem |
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