Dynamic control of the space tethered system
We discuss the problem of simultaneous dynamical stabilization and suppression of transverse and longitudinal vibrations of the space tethered system deployed along a certain trajectory. The dynamics of the system is described by a system of nonlinear partial differential equations for the longitudi...
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| Veröffentlicht in: | Journal of sound and vibration 2017-02, Vol.389, p.41-51 |
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| container_title | Journal of sound and vibration |
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| creator | Malashin, A.A. Smirnov, N.N. Bryukvina, O.Yu Dyakov, P.A. |
| description | We discuss the problem of simultaneous dynamical stabilization and suppression of transverse and longitudinal vibrations of the space tethered system deployed along a certain trajectory. The dynamics of the system is described by a system of nonlinear partial differential equations for the longitudinal and transverse waves and we consider a non-classical version of the problem with one moving boundary. We formulate a mathematical model and perform the analytic and numerical analysis of the boundary control problem based on the Lyapunov method. A scheme of the deployment mechanism is suggested. It includes a control torque and transverse displacement of the boundary and ensures stable deployment of the whole system.
•Boundary control of transverse and longitudinal vibrations.•Suppression of vibrations, asymptotic stability of the tethered system's deployment.•Efficient mechanism for stable deployment.•Dynamics of the tether is described by PDEs.•Numerical calculations prove asymptotic stability of the deployment process. |
| doi_str_mv | 10.1016/j.jsv.2016.11.026 |
| format | Article |
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•Boundary control of transverse and longitudinal vibrations.•Suppression of vibrations, asymptotic stability of the tethered system's deployment.•Efficient mechanism for stable deployment.•Dynamics of the tether is described by PDEs.•Numerical calculations prove asymptotic stability of the deployment process.</description><subject>Asymptotic methods</subject><subject>Asymptotic stability</subject><subject>Boundary control</subject><subject>Dynamic control</subject><subject>Lyapunov method</subject><subject>Mathematical models</subject><subject>Nonlinear differential equations</subject><subject>Nonlinear equations</subject><subject>Nonlinear transverse and longitudinal vibration</subject><subject>Numerical analysis</subject><subject>Partial differential equations</subject><subject>Transverse waves</subject><subject>Vibration</subject><issn>0022-460X</issn><issn>1095-8568</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKs_wNuCV3fNZJP9wJPUTyh4UfAWtpMJ7tJuapIW-u9NWc-e5j28z8zwMHYNvAAO1d1QDGFfiBQLgIKL6oTNgLcqb1TVnLIZ50LksuJf5-wihIFz3spSztjt42HsNj1m6Mbo3TpzNovflIVth5RFStmTycIhRNpcsjPbrQNd_c05-3x--li85sv3l7fFwzLHUqiYo2gaZTqJnZSKLEmsFYAhMCBtbaEiU9aooJKAYmVRrRoUtlTcQFsTYjlnN9PerXc_OwpRD27nx3RSC66UalVdV6kFUwu9C8GT1Vvfbzp_0MD1UYoedJKij1I0gE5SEnM_MZTe3_fkdcCeRiTTe8Kojev_oX8BZ_1pew</recordid><startdate>20170217</startdate><enddate>20170217</enddate><creator>Malashin, A.A.</creator><creator>Smirnov, N.N.</creator><creator>Bryukvina, O.Yu</creator><creator>Dyakov, P.A.</creator><general>Elsevier Ltd</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>KR7</scope></search><sort><creationdate>20170217</creationdate><title>Dynamic control of the space tethered system</title><author>Malashin, A.A. ; Smirnov, N.N. ; Bryukvina, O.Yu ; Dyakov, P.A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-c2885da4ca445efe4c7511de1d14f7f16ed37c51641c2bfc5b8c2f350d197ecc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic stability</topic><topic>Boundary control</topic><topic>Dynamic control</topic><topic>Lyapunov method</topic><topic>Mathematical models</topic><topic>Nonlinear differential equations</topic><topic>Nonlinear equations</topic><topic>Nonlinear transverse and longitudinal vibration</topic><topic>Numerical analysis</topic><topic>Partial differential equations</topic><topic>Transverse waves</topic><topic>Vibration</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Malashin, A.A.</creatorcontrib><creatorcontrib>Smirnov, N.N.</creatorcontrib><creatorcontrib>Bryukvina, O.Yu</creatorcontrib><creatorcontrib>Dyakov, P.A.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Civil Engineering Abstracts</collection><jtitle>Journal of sound and vibration</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Malashin, A.A.</au><au>Smirnov, N.N.</au><au>Bryukvina, O.Yu</au><au>Dyakov, P.A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dynamic control of the space tethered system</atitle><jtitle>Journal of sound and vibration</jtitle><date>2017-02-17</date><risdate>2017</risdate><volume>389</volume><spage>41</spage><epage>51</epage><pages>41-51</pages><issn>0022-460X</issn><eissn>1095-8568</eissn><abstract>We discuss the problem of simultaneous dynamical stabilization and suppression of transverse and longitudinal vibrations of the space tethered system deployed along a certain trajectory. The dynamics of the system is described by a system of nonlinear partial differential equations for the longitudinal and transverse waves and we consider a non-classical version of the problem with one moving boundary. We formulate a mathematical model and perform the analytic and numerical analysis of the boundary control problem based on the Lyapunov method. A scheme of the deployment mechanism is suggested. It includes a control torque and transverse displacement of the boundary and ensures stable deployment of the whole system.
•Boundary control of transverse and longitudinal vibrations.•Suppression of vibrations, asymptotic stability of the tethered system's deployment.•Efficient mechanism for stable deployment.•Dynamics of the tether is described by PDEs.•Numerical calculations prove asymptotic stability of the deployment process.</abstract><cop>Amsterdam</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.jsv.2016.11.026</doi><tpages>11</tpages></addata></record> |
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| issn | 0022-460X 1095-8568 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Asymptotic methods Asymptotic stability Boundary control Dynamic control Lyapunov method Mathematical models Nonlinear differential equations Nonlinear equations Nonlinear transverse and longitudinal vibration Numerical analysis Partial differential equations Transverse waves Vibration |
| title | Dynamic control of the space tethered system |
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