Papers by marcela zuccalli
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Journal of Geometric Mechanics
In the context of underactuated Hamiltonian systems defined by simple Hamiltonian functions, the ... more 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 configuration 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 \begin{document}$ C^{\infty} $\end{document} 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 ...
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Journal of Geometric Mechanics
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International Journal of Geometric Methods in Modern Physics, Jan 21, 2020
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Quarterly of Applied Mathematics, Apr 7, 2005
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Journal of Geometry and Physics
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Journal of Geometric Mechanics, 2016
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The Journal of Geometric Mechanics, 2010
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Papers by marcela zuccalli