2014
DOI: 10.1088/1674-1056/23/7/070201
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Symmetries and variational calculation of discrete Hamiltonian systems

Abstract: We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.

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Cited by 5 publications
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“…where μ represents the smoothing weight coefficient [39], which refers to the proportion of the speed smooth term. en, using the variational calculation [40], the Laplacian operator can be obtained approximately by making difference between the velocity of a pixel point and the average velocity of its surrounding pixel points. us, we can use the iterative method to solve the optical flow equation ( 1), where n represents the number of iterations.…”
Section: Moving Vehicle Detection Based On the Optical Flow Methodsmentioning
confidence: 99%
“…where μ represents the smoothing weight coefficient [39], which refers to the proportion of the speed smooth term. en, using the variational calculation [40], the Laplacian operator can be obtained approximately by making difference between the velocity of a pixel point and the average velocity of its surrounding pixel points. us, we can use the iterative method to solve the optical flow equation ( 1), where n represents the number of iterations.…”
Section: Moving Vehicle Detection Based On the Optical Flow Methodsmentioning
confidence: 99%