弹性固体中旋转波的精确描述
Exact Description of Rotational Waves in an Elastic Solid
摘要：
弹性固体中横波的传统描述受到旋转梯度极小的假设的限制。通过假设一个线性响应的变化方向，我们推导出一个严格的描述一类限制的旋转波在一个理想的各向同性弹性固体。其结果是一个非线性方程表示的狄拉克双旋量。这个结果提供了相对论量子力学动力学的一个简单的经典解释。我们构造一个形式为L=-E+U+K=0的拉格朗日量，其中E是总能量，U是势能，K是动能。
英文摘要：
Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a restricted class of rotational waves in an ideal isotropic elastic solid. The result is a nonlinear equation expressed in terms of Dirac bispinors. This result provides a simple classical interpretation of relativistic quantum mechanical dynamics. We construct a Lagrangian of the form L=-E+U+K=0, where E is the total energy, U is the potential energy, and K is the kinetic energy.
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