分数阶驱动阻尼振子

同时受弱线性和非线性阻尼力作用的谐振子振幅衰减

The amplitude decay of a harmonic oscillator damped simultaneously by weak linear and nonlinear damping forces

本文基于能量耗散率与阻尼力功率关系，推导恒幅、线性和二次速度阻尼共同作用下弱阻尼谐振子的振幅衰减近似解，并经数值解验证其在实验相关参数范围内准确可靠。

重访阻尼谐振子：通往平衡的最快路径

Damped harmonic oscillator revisited: the fastest route to equilibrium

本文证明在有限能量分辨率下，最优欠阻尼解通常比临界阻尼解更快达到平衡阈值，并指出特定初始条件下过阻尼解例外更快，且实验验证了部分结论。

Revisiting the Coulomb-Damped Harmonic Oscillator

The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is…

带阻尼的Duffing振子的解与Lagrangian表示

On the solution and Lagrangian representation of Duffing oscillator with damping

本文在弱阻尼极限下通过去除阻尼项得到阻尼Duffing方程的解析解，分析阻尼对相路径的畸变影响，并构造无阻尼与阻尼情形的Lagrangian表示，为系统量子化提供基础。

基于诺特对称原理的阻尼Pinney方程研究

On the Damped Pinney Equation from Noether Symmetry Principles

本文针对阻尼Pinney方程的多版本问题，以含时谐振子的诺特定理为指导，推导出基于诺特对称的阻尼Pinney方程，并将结果推广至一般非线性阻尼Ermakov系统，证明可通过时间重标度消去方程中的阻尼项。

Hamiltonian and Linear-Space Structure for Damped Oscillators: I. General Theory

The phase space of $N$ damped linear oscillators is endowed with a bilinear map under which the evolution operator is symmetric. This analog of self-adjointness allows properties familiar from conservative systems to be recovered, e.g., eigenvectors are "orthogonal" under the bilinear map and obey sum rules, initial-value problems are readily solved and perturbation theory applies to the_complex_ eigenvalues. These concepts are conveniently represented in a biorthogonal basis.

Hamiltonian and Linear-Space Structure for Damped Oscillators: II. Critical Points

The eigenvector expansion developed in the preceding paper for a system of damped linear oscillators is extended to critical points, where eigenvectors merge and the time-evolution operator $H$ assumes a Jordan-block structure. The representation of the bilinear map is obtained in this basis. Perturbations $εΔH$ around an $M$-th order critical point generically lead to eigenvalue shifts $\simε^{1/M}$ dependent on only_one_ matrix element, with the $M$ eigenvalues splitting in equiangular directions in the complex plane. Small denominators near criticality are shown to cancel.

利用能量耗散率和一个简单技巧对弱阻尼谐振子的振幅与能量衰减进行建模

Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick

本文提出一种无需求解运动方程即可建模弱阻尼谐振子振幅指数衰减和能量衰减的简单方法，通过叠加相同能量下两组初始条件的能量耗散率得到一阶微分方程，结果与精确解高度吻合。

运动杆问题：机电阻尼振荡器

The moving bar problem: an electromechanical damped oscillator

本文拓展经典运动杆问题，保留自感磁场建立机电耦合模型，推导等效RLC电路，数值积分验证解析结果并确定阻尼行为转换点。

Fractional Oscillator -- Harmonic Oscillator with Memory Effects

The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.

补遗：利用能量耗散率和一个简单技巧建模弱阻尼谐振子的振幅与能量衰减（2025 Eur. J. Phys. 46(1) 015004）

Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)

本研究调整粘性阻尼的已有方法，推导滑动摩擦、空气阻力两种阻尼下弱阻尼谐振子的近似振幅衰减，得到对应一阶微分方程与时变振幅，适合大一本科生理解掌握。

理解具有密集模态的非经典阻尼线性振子中的模态相互作用

Understanding Modal Interactions in Non-classically Damped Linear Oscillators with Closely Spaced Modes

本文通过两自由度非经典阻尼耦合振子研究密集模态下的模态相互作用，提出以耦合与阻尼非比例性之比作为临界参数，揭示两种动力学状态及其拍现象差异，并给出系统辨识与降阶建模框架。

Eigenvector Expansion and Petermann Factor for Ohmically Damped Oscillators

Correlation functions $C(t) \sim <ϕ(t)ϕ(0)>$ in ohmically damped systems such as coupled harmonic oscillators or optical resonators can be expressed as a single sum over modes $j$ (which are not power-orthogonal), with each term multiplied by the Petermann factor (PF) $C_j$, leading to "excess noise" when $|C_j| > 1$. It is shown that $|C_j| > 1$ is common rather than exceptional, that $|C_j|$ can be large even for weak damping, and that the PF appears in other processes as well: for example, a time-independent perturbation $\sim\ep$ leads to a frequency shift $\sim \ep C_j$. The coalescence o…