苏州科技大学学报（自然科学版）2026，Vol.43Issue(3)：30-37,8.DOI:10.12084/j.issn.2096-3289.2026.03.003
受迫Birkhoff系统的Herglotz动力学及其Noether对称性与守恒量
Herglotz dynamics of forced Birkhoffian systems and their Noether symmetry and conserved quantity
摘要
Abstract
Birkhoffian mechanics is a natural extension of Hamiltonian mechanics to general symplectic manifolds.The Herglotz variational principle defines the action via a differential equation,providing a variational framework for handling dissipative systems.This paper combines the two approaches to study Herglotz dynamics and its symmetries within forced Birkhoffian systems,thereby offering a new pathway for analyzing dynamical problems under the coupled influence of external excitation and dissipation.First,the Herglotz variational principle for forced Birkhof-fian systems was established,from which the Herglotz-type Pfaff-Birkhoff-d'Alembert differential variational prin-ciple and Herglotz's equations were derived.By introducing infinitesimal transformations,the total variational for-mulas for the Pfaff-Herglotz action of forced Birkhoffian systems were obtained,the Herglotz-type Noether symme-try was defined,and its determining equations were formulated.On this basis,the Noether theorem and its inverse theorem were formulated and proved,yielding the corresponding Herglotz-type Noether conserved quantities for the systems.Finally,a linearly damped forced oscillator was taken as an example to illustrate how to apply the obtained theorems to analyze the Noether symmetry and conserved quantities of the system,thereby verifying the effectiveness and applicability of the proposed method.关键词
受迫Birkhoff系统/Herglotz方程/Noether对称性/守恒量Key words
forced Birkhoffian system/Herglotz equation/Noether symmetry/conserved quantity分类
数理科学引用本文复制引用
张毅..受迫Birkhoff系统的Herglotz动力学及其Noether对称性与守恒量[J].苏州科技大学学报（自然科学版）,2026,43(3):30-37,8.基金项目
国家自然科学基金面上项目(12272248) （12272248）
