Artículo
Explicit solutions of the kinetic and potential matching conditions of the energy shaping method
Fecha de publicación:
12/2021
Editorial:
American Institute of Mathematical Sciences
Revista:
Journal of Geometric Mechanics
ISSN:
1941-4889
e-ISSN:
1941-4897
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Articulos(CCT - PATAGONIA NORTE)
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Articulos de CTRO.CIENTIFICO TECNOL.CONICET - PATAGONIA NORTE
Citación
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
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