论文标题
关于惯性的Helmholtz-Hodge分解，在离散的本地参考框架上
On Helmholtz-Hodge decomposition of inertia on a discrete local frame of reference
论文作者
论文摘要
惯性参考框架的概念被放弃了，我用一个局部参考框架代替了它的基本力学定律。因果关系的遥远相互作用是通过从一个局部参考框架到另一个局部参考框架的波传播来建模的。直接段上运动方程的推导作用表达了适当的加速度作为施加的加速度的总和，以正交局部局部Helmholtz-hodge分解的形式，以一种无差异和另一种卷曲的贡献。我以标量电位的梯度和向量电位的双重卷曲的形式写了惯性术语。所采用的形式主义为根据潜在的重新制定了重新制定材料衍生物的道路，并使我能够从连续力学中删除虚拟力量。除了每单位质量和加速度的能量保护外，还使用了在恒定角速度下旋转的离散运动方程，以恒定角速度旋转来保护质量的角动量。该方程式中的所有变量仅以两个基本单元（即长度和时间的单元）表示。
The notion of inertial reference frame is abandoned and I replaced it by a local reference frame on which the fundamental law of mechanics is expressed. The distant interactions of cause and effect are modeled by the propagation of waves from one local reference frame to another. The derivation of the equation of motion on a straight segment serves to express the proper acceleration as the sum of the accelerations imposed on it, in the form of an orthogonal local Helmholtz-Hodge decomposition, in one divergence-free and another curl-free contribution. I wrote the inertia term in the form of a gradient of a scalar potential and a dual curl of a vector potential. The adopted formalism opens the way to a reformulation of the material derivative in terms of potentials and allows me to remove the fictitious forces from continuum mechanics. The discrete equation of motion, invariant by rotation at constant angular velocity, is used to conserve the angular momentum per unit of mass, in addition to the conservation of energy per unit of mass and acceleration. All the variables in this equation are expressed only with two fundamental units, those of length and time.
