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<p>In this paper, we introduce some different definitions of symmetries for Hamiltonian, Almost-Hamiltonian, Lagrangian systems and investigate how to find the conserved quantities of each system by using them. Moreover, we investigate what form generalized infinitesimal symmetries of the <i>C</i>-integrable, non-degenerate Hamiltonian system have, and show that the set of them is generally not a commutative Lie algebra. We also review well-known results (Noether theorem and so on) and properties about the symmetries of Hamiltonian, almost-Hamiltonian and Lagrangian systems, and then new relationships between some kinds of symmetries that we define and conserved quantities are established.</p>

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Conserved Quantities, Symmetries of (Almost-)Hamiltonian and Lagrangian Systems

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Xuefeng Zhao,
  • Yong Li

摘要

In this paper, we introduce some different definitions of symmetries for Hamiltonian, Almost-Hamiltonian, Lagrangian systems and investigate how to find the conserved quantities of each system by using them. Moreover, we investigate what form generalized infinitesimal symmetries of the C-integrable, non-degenerate Hamiltonian system have, and show that the set of them is generally not a commutative Lie algebra. We also review well-known results (Noether theorem and so on) and properties about the symmetries of Hamiltonian, almost-Hamiltonian and Lagrangian systems, and then new relationships between some kinds of symmetries that we define and conserved quantities are established.