Intrinsic thermal fluctuations within a real solid challenge the rigid body assumption that is central to Euler’s equations for the motion of a free body. Recently, we have introduced a dissipative and stochastic version of Euler’s equations in a thermodynamically consistent way (European Journal of Mechanics – A/Solids 103, 105,184 (2024)). This framework describes the evolution of both orientation and shape of a free body, incorporating internal thermal fluctuations and their concomitant dissipative mechanisms. In the present work, we demonstrate that, in the absence of angular momentum, the theory predicts that the principal axes unit vectors of a body undergo an anisotropic Brownian motion on the unit sphere, with the anisotropy arising from the body’s varying moments of inertia. The resulting equilibrium time correlation function of the principal eigenvectors decays exponentially. This theoretical prediction is confirmed in molecular dynamics simulations of small bodies. The comparison of theory and equilibrium MD simulations allow us to measure the orientational diffusion tensor. We then use this information in the Stochastic Dissipative Euler’s Equations, to describe a non-equilibrium situation of a body spinning around the unstable intermediate axis. The agreement between theory and simulations is excellent, offering a validation of the theoretical framework.

中文翻译：

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自由体的随机耗散欧拉方程


真实固体中的内禀热波动挑战了刚体假设，该假设是自由体运动欧拉方程的核心。最近，我们以热力学一致的方式引入了欧拉方程的耗散和随机版本 （European Journal of Mechanics – A/Solids 103， 105,184 （2024））。该框架描述了自由体的方向和形状的演变，包括内部热波动及其伴随的耗散机制。在本工作中，我们证明了在没有角动量的情况下，该理论预测物体的主轴单位矢量在单位球面上发生各向异性布朗运动，各向异性由物体的变化惯性矩产生。主特征向量的平衡时间相关函数呈指数衰减。这一理论预测在小天体的分子动力学模拟中得到了证实。理论和平衡 MD 模拟的比较使我们能够测量取向扩散张量。然后，我们在随机耗散欧拉方程中使用这些信息来描述物体围绕不稳定的中间轴旋转的非平衡情况。理论与仿真之间的一致性非常好，为理论框架提供了验证。