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A Simple Method for Impasse Points Detection in Nonlinear Electrical Circuits (2018)

Diana Leonor Kleiman, María del Rosario Etchechoury, and Paul Puleston

Hindawi

In: Mathematical Problems in Engineering

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Publication Date: 2018-03-06

Description: In a nonlinear system, impasse points are singularities beyond which solutions are not continuable. In this article, we study two families of nonlinear electrical circuits, which can be represented by nonlinear Implicit Differential Equations. We set conditions that ensure the existence of impasse points in both families of circuits. In the literature, there exist general results to analyse the presence of such singularities in given differential equations of this type. However, the method proposed in this work allows detecting their existence in these electrical topologies in an extremely straightforward way, as illustrated by the examples of application.

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Electronic ISSN: 1563-5147

Topics: Mathematics , Technology

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A Note about Certain Arbitrariness in the Solution of the Homological Equation in Deprit’s Method (2015)

Juan Félix San-Juan, Rosario López, Iván Pérez, and Montserrat San-Martín

Hindawi

In: Mathematical Problems in Engineering

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Publication Date: 2015-03-03

Description: Deprit’s method has been revisited in order to take advantage of certain arbitrariness arising when the inverse of the Lie operator is applied to obtain the generating function of the Lie transform. This arbitrariness is intrinsic to all perturbation techniques and can be used to demonstrate the equivalence among different perturbation methods, to remove terms from the generating function of the Lie transform, or to eliminate several angles simultaneously in the case of having a degenerate Hamiltonian.

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A Note about Certain Arbitrariness in the Solution of the Homological Equation in Deprit’s Method (2015)

San-Juan, Juan Félix ; López, Rosario ; Pérez, Iván ; [et al.]

Hindawi

In: Mathematical Problems in Engineering. 2015; 2015: 1-10. Published 2015 Jan 01. doi: 10.1155/2015/982857.

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Publication Date: 2015-01-01

Description: Deprit’s method has been revisited in order to take advantage of certain arbitrariness arising when the inverse of the Lie operator is applied to obtain the generating function of the Lie transform. This arbitrariness is intrinsic to all perturbation techniques and can be used to demonstrate the equivalence among different perturbation methods, to remove terms from the generating function of the Lie transform, or to eliminate several angles simultaneously in the case of having a degenerate Hamiltonian.

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Electronic ISSN: 1563-5147

Topics: Mathematics , Technology

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Higher-Order Analytical Attitude Propagation of an Oblate Rigid Body under Gravity-Gradient Torque (2012)

San-Juan, Juan F. ; López, Luis M. ; López, Rosario

Hindawi

In: Mathematical Problems in Engineering. 2012; 2012: 1-15. Published 2012 Jan 01. doi: 10.1155/2012/123138.

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Publication Date: 2012-01-01

Description: A higher-order perturbation theory for the rotation of a uniaxial satellite under gravity-gradient torque demonstrates that known special configurations of the attitude dynamics at which the satellite rotates, on average, as in a torque-free state, are only the result of an early truncation of the secular frequencies of motion. In addition to providing a deeper insight into the dynamics, the higher order of the analytical solution makes it competitive when compared with the long-term numerical integration of the equations of motion.

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Nonlinear Systems: Asymptotic Methods, Stability, Chaos, Control, and Optimization (2011)

Silva, Geraldo Nunes ; de Pinho, Maria do Rosário ; Teixeira, Marco Antonio ; [et al.]

Hindawi

In: Mathematical Problems in Engineering. 2011; 2011: 1-4. Published 2011 Jan 01. doi: 10.1155/2011/498751.

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Publication Date: 2011-01-01

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Electronic ISSN: 1563-5147

Topics: Mathematics , Technology

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A Simple Method for Impasse Points Detection in Nonlinear Electrical Circuits (2018)

Kleiman, Diana Leonor ; Etchechoury, María del Rosario ; Puleston, Paul

Hindawi

In: Mathematical Problems in Engineering. 2018; 2018: 1-7. Published 2018 Jan 01. doi: 10.1155/2018/2613890.

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Publication Date: 2018-01-01

Description: In a nonlinear system, impasse points are singularities beyond which solutions are not continuable. In this article, we study two families of nonlinear electrical circuits, which can be represented by nonlinear Implicit Differential Equations. We set conditions that ensure the existence of impasse points in both families of circuits. In the literature, there exist general results to analyse the presence of such singularities in given differential equations of this type. However, the method proposed in this work allows detecting their existence in these electrical topologies in an extremely straightforward way, as illustrated by the examples of application.

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Electronic ISSN: 1563-5147

Topics: Mathematics , Technology

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Fractional Order Calculus: Basic Concepts and Engineering Applications (2010)

Gutiérrez, Ricardo Enrique ; Rosário, João Maurício ; Tenreiro Machado, José

Hindawi

In: Mathematical Problems in Engineering. 2010; 2010: 1-19. Published 2010 Jan 01. doi: 10.1155/2010/375858.

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Publication Date: 2010-01-01

Description: The fractional order calculus (FOC) is as old as the integer one although up to recently its application was exclusively in mathematics. Many real systems are better described with FOC differential equations as it is a well-suited tool to analyze problems of fractal dimension, with long-term “memory” and chaotic behavior. Those characteristics have attracted the engineers' interest in the latter years, and now it is a tool used in almost every area of science. This paper introduces the fundamentals of the FOC and some applications in systems' identification, control, mechatronics, and robotics, where it is a promissory research field.

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