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Non-Linear Dynamics with Non-Standard Lagrangians

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Abstract

Two new actions being of a non-natural class \({S = \int {e^{L(q, \dot {q}, t)}dt}}\) and \({S = \int {L^{1 + \gamma }(q, \dot {q}, t)dt}, \gamma \in {\mathbb{R}}}\) with non-standard Lagrangians are introduced. It is demonstrated that nonlinear systems holding new dynamical properties may be obtained. Several constrained Lagrangians systems have been identified to possess attractive properties. Additional features are explored and discussed in some details.

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Authors and Affiliations

  1. Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang, 641112, Sichuan, China

    Ahmad Rami El-Nabulsi

  2. College of Mathematics and Information Science, Neijiang Normal University, Neijiang, 641112, Sichuan, China

    Ahmad Rami El-Nabulsi

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  1. Ahmad Rami El-Nabulsi
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Correspondence to Ahmad Rami El-Nabulsi.

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El-Nabulsi, A.R. Non-Linear Dynamics with Non-Standard Lagrangians. Qual. Theory Dyn. Syst. 12, 273–291 (2013). https://doi.org/10.1007/s12346-012-0074-0

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