摩擦斜向颗粒碰撞中切向与运动学恢复系数的非唯一性
Nonuniqueness of Tangential and Kinematic Restitution in Frictional Oblique Particle Impacts
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中文总结 AI 辅助
该研究系统分析摩擦圆盘的切向与运动学恢复系数随冲击角、摩擦系数及初始角速度的变化规律，揭示其非单调非线性特性及非唯一性，为颗粒碰撞的相关研究提供了关键依据。
中文摘要 AI 辅助
我们系统研究了耗散摩擦圆盘的不同恢复系数随冲击角θ、摩擦系数μ及初始角速度ω_in的变化规律。观察到切向恢复系数e_T和运动学恢复系数e_kin呈现非单调非线性行为，在与μ相关的θ值处存在明显极小值，且大θ时所有μ下均收敛于纯滚动与纯滑动情形的边界。改变法向耗散相互作用会影响大θ时的μ收敛，并导致低θ时出现收敛。初始角速度ω_in的存在可显著改变e_T在陡冲击下的函数行为，轻微改变e_kin的幅值，而摩擦仅起次要作用。总体而言，我们的结果表明，e_T或e_kin的任一特定值都具有高度情境性，可同时描述完全不同的接触构型。
英文摘要
We systematically investigate the different coefficients of restitution of a dissipative, frictional disc as a function of the impact angle $θ$, the friction coefficient $μ$ and initial rotation $ω_{\mathrm{in}}$. We observe a non-monotonic, non-linear behaviour of $e_{\mathrm{T}}$ and $e_{\mathrm{kin}}$ with a clear minimum at $μ$-dependent values of $θ$ and a convergence for all $μ$ at large $θ$, bounded by the cases of pure rolling and pure sliding. Changing the dissipative normal interaction affects the $μ$ convergence at large $θ$ and leads to a convergence at low $θ$. The presence of initial angular velocity $ω_{\mathrm{in}}$ can significantly alter the functional behaviour of $e_{\mathrm{T}}$ at steep impacts and slightly change the magnitude of $e_{\mathrm{kin}}$, with friction playing only a minor role. Overall, our results indicate that any specific value of $e_{\mathrm{T}}$ or $e_{\mathrm{kin}}$ is highly situational and can simultaneously describe entirely different contact configurations.
