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dc.contributor.author
Grillo, Sergio Daniel
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dc.contributor.author
Zuccalli, Marcela
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dc.contributor.author
Salomone, Leandro Martin
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dc.date.available
2023-08-15T13:54:02Z
dc.date.issued
2021-12
dc.identifier.citation
Grillo, Sergio Daniel; Zuccalli, Marcela; Salomone, Leandro Martin; Explicit solutions of the kinetic and potential matching conditions of the energy shaping method; American Institute of Mathematical Sciences; Journal of Geometric Mechanics; 13; 4; 12-2021; 629-646
dc.identifier.issn
1941-4889
dc.identifier.uri
http://hdl.handle.net/11336/208304
dc.description.abstract
In the context of underactuated Hamiltonian systems defined by simple Hamiltonian functions, the matching conditions of the energy shaping method split into two decoupled subsets of equations: The kinetic and potential equations. The unknown of the kinetic equation is a metric on the configura- tion space of the system, while the unknown of the potential equation are the same metric and a positive-definite function around some critical point of the Hamiltonian function. In this paper, assuming that a solution of the kinetic equation is given, we find conditions (in the C1 category) for the existence of positive-definite solutions of the potential equation and, moreover, we present a procedure to construct, up to quadratures, some of these solutions. In order to illustrate such a procedure, we consider the subclass of systems with one degree of underactuation, where we find in addition a concrete formula for the general solution of the kinetic equation. As a byproduct, new global and local expressions of the matching conditions are presented in the paper.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Institute of Mathematical Sciences
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dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
CLOSED-LOOP SYSTEMS
dc.subject
ENERGY SHAPING
dc.subject
HAMILTONIAN SYSTEMS
dc.subject
INTEGRATION BY QUADRATURES
dc.subject
UNDERACTUATED SYSTEMS
dc.subject.classification
Matemática Aplicada
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Explicit solutions of the kinetic and potential matching conditions of the energy shaping method
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-08-14T17:35:37Z
dc.identifier.eissn
1941-4897
dc.journal.volume
13
dc.journal.number
4
dc.journal.pagination
629-646
dc.journal.pais
Estados Unidos
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dc.description.fil
Fil: Grillo, Sergio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
dc.description.fil
Fil: Zuccalli, Marcela. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina
dc.description.fil
Fil: Salomone, Leandro Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina
dc.journal.title
Journal of Geometric Mechanics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/jgm.2021022
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3934/jgm.2021022
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