New non-standard Lagrangians for the Lienard-type equations
Applied Mathematics Letters. 2017. Vol. 63. P. 124-129.
Кудряшов Н. А., Sinelshchikov D.
Liénard-type equations are used for the description of various phenomena in physics and other fields of science. Here we find a new family of the Liénard-type equations which admits a non-standard autonomous Lagrangian. As a by-product we obtain autonomous first integrals for each member of this family of equations. We also show that some of the previously known conditions for the existence of a non-standard Lagrangian for the Liénard-type equations follow from the linearizability of the corresponding equation via nonlocal transformations.
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We study a family of the Lienard-type equations, which can be transformed via the generalized Sundman transformations into a particular case of Painleve-Gambier equation XXVII. We show that this equation of the Painleve-Gambier type admits an autonomous Lagrangian, Jacobi last multiplier and first integral. As a consequence, we obtain that the corresponding family of Lienard-type ...
Added: February 11, 2019
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Added: October 16, 2018
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, , Успехи современной радиоэлектроники 2018 № 10 С. 75-82
In this paper, the application of Lagrangian mechanic principles is introduced for dynamic analysis of lumped-element electric circuits containing resistors and sources of independent voltages and currents. It was discussed that formal analogy between the generalized coordinates of masses in classical mechanics and charges in electric circuit theory allows making up a clear qualitative interpretation ...
Added: February 5, 2019