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Updated: Aug 30, 2025

The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
On controlled Hamilton and Hamilton-Jacobi differential equations of higher-order
Savin Treanţă1,2,3, Kamsing Nonlaopon4, Muhammad Bilal Khan5
1Department of Applied Mathematics, University Politehnica of Bucharest, 060042, Bucharest, Romania.
Abstract:
In this paper, we investigate the nonlinear dynamics associated with controlled Lagrangians involving higher-order derivatives. More precisely, we establish the controlled higher-order Hamilton ordinary differential equations (ODEs) and Hamilton-Jacobi partial differential equation (PDE) for the considered class of Lagrangians governed by higher-order derivatives of the state variables. Moreover, we formulate and prove an invariance result with respect to the state variable. In addition, in order to validate the theoretical results and to highlight their effectiveness, some illustrative applications are presented.
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