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Symmetry, Volume 18, Issue 6 (June 2026) – 1 article

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16 pages, 270 KB  
Article
Lie Symmetries and Invariants of General Time-Dependent Quadratic Hamiltonian System
by Kyu Hwang Yeon, Van Huy Pham and Keun Ho Ryu
Symmetry 2026, 18(6), 880; https://doi.org/10.3390/sym18060880 (registering DOI) - 22 May 2026
Abstract
Eight Lie algebras of point-symmetric groups and corresponding generators are admitted by the equation of motion, which is obtained from a general time-dependent quadratic Hamiltonian. We show that invariant quantities obtained by eight algebraic generators are the Wronskian constant, three conserved quantities, which [...] Read more.
Eight Lie algebras of point-symmetric groups and corresponding generators are admitted by the equation of motion, which is obtained from a general time-dependent quadratic Hamiltonian. We show that invariant quantities obtained by eight algebraic generators are the Wronskian constant, three conserved quantities, which are time-dependent quadratic forms in position and momentum, and trivial, 0. All obtained invariant quantities are represented by auxiliary conditions, which are two linearly independent solutions of a homogeneous differential equation of the equations of motion. Invariant variables associated with an invariant consisting of the linearity of x and p are defined. It shows that, if the motion of the system is oscillatory, the Poisson bracket of the two invariant variables is obtained as i, and in the case of monotonic motion, it is obtained as 1. Full article
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