一种通用的阻尼模型--修正的库仑摩擦模型

具有摩擦阻尼的运动方程的哈密顿量

Hamiltonians representing equations of motion with damping due to friction

假设$H(q,p)$是流形$M$上的哈密顿量，并且瑞利耗散函数$\tilde L(q,\dot q)$满足与流形$M$上的拉格朗日量相同的假设。我们提供了一个哈密顿框架，给出了方程$\dot q = \frac{\partial H}{\partial p}(q,p), \quad \dot p = - \frac{\partial H}{\partial q}(q,p) - \frac{\partial \tilde L}{\partial \dot q}(q,\dot q)$。该方法是将$M$嵌入到一个更大的框架中，其中运动驱动负半线上的波动方程，其中波中的能量表示从运动中带走的热量。我们得到一个版本的Nöther定理，是有效的耗散系统。我们还表明，这一框架符合广泛持有的观点，如何哈密顿动力学可以导致“时间之箭。"

带摩擦的滑动与最速降线问题

Sliding with Friction and The Brachistochrone Problem

本文研究了考虑库仑摩擦力时粒子在重力场中沿可微曲线的运动，给出了推广摆线的最优曲线参数方程，并通过Mathcad数值计算验证其为带库仑摩擦的最速降线。

阻尼谐振子再探讨：Coulomb、Stokes和Newton阻尼情况下能量衰减的新方法

Damped harmonic oscillator revisited: a new approach to energy decay in the case of Coulomb, Stokes, and Newton damping

本文提出了一种新方法，用于描述Coulomb、Stokes和Newton阻尼机制下谐振子的能量衰减，通过直接分析框架和精确解推导，为物理教学提供理论支持。

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…

ISS-Based Robustness to Various Neglected Damping Mechanisms for the 1-D Wave PDE

This paper is devoted to the study of the robustness properties of the 1-D wave equation for an elastic vibrating string under four different damping mechanisms that are usually neglected in the study of the wave equation: (i) friction with the surrounding medium of the string (or viscous damping), (ii) thermoelastic phenomena (or thermal damping), (iii) internal friction of the string (or Kelvin-Voigt damping), and (iv) friction at the free end of the string (the so-called passive damper). The passive damper is also the simplest boundary feedback law that guarantees exponential stability for …

摩擦力和保守力组合在耗散Lagrange-Hamilton形式下的表达式

Expressions for frictional and conservative force combinations within the dissipative Lagrange-Hamilton formalism

耗散拉格朗日和哈密顿具有库仑，粘性和二次阻尼，连同重力和弹性项的形式主义，保持哈密顿作为一个常数的运动。他们的推导也显示。由此产生的L和H可能在探索新类型的阻尼量子系统中证明是有用的。

包括阻尼和陀螺效应的尖叫噪声和模式耦合不稳定性的分析

Analysis of squeal noise and mode coupling instabilities including damping and gyroscopic effects

本文从摩擦引起的模态耦合不稳定性的角度研究了汽车离合器尖叫噪声。首先，提出了一个自耦合模型，该模型显示了源自摩擦力的非保守循环效应。其次，通过确定系统线性化方程的特征值来研究平衡点的稳定性。的循环和陀螺仪的行动的影响进行检查分析和数值计算，以确定其对稳定区域的影响。单独和组合的影响进行了分析，并没有结构阻尼和重要的信息，每个参数的作用和它们之间的相互作用，对整体稳定性。不仅是结构阻尼被证明是首要的重要性，在许多以前的作品中报道，这篇文章还强调了一个特殊的关系与陀螺效应。讨论了优化稳定范围和鲁棒性对系统参数不确定性的方法，给出了实用的设计建议。

Research on rolling friction's dependence on ball bearings' radius

There are two alternative historical laws of rolling resistance formulated by French scientist Coulomb and Dupuit. It has been decided to verify experimentally again, which of these laws describes freely rolling ball bearings on a hard surface better. An inducement to carrying out the measurements was the idea of the constant thickness of roadbed, which is consistent with Dupuit's theory. Measurements have been done using the damped oscillations in the pendulum bearings. Results have shown better consistency with the Coulomb's theory with small, but measurable deviations. These deviations were…