关于离散局部参考系上惯量的Helmholtz-Hodge分解
On Helmholtz-Hodge decomposition of inertia on a discrete local frame of reference
摘要：
惯性参考系的概念被抛弃了，我用局部参考系来代替它，力学的基本定律就是在这个局部参考系上表达的。通过波从一个局部参考系到另一个局部参考系的传播来模拟远距离的因果相互作用。在直段上的运动方程的推导用于将固有加速度表示为施加在其上的加速度之和，以正交局部亥姆霍兹-霍奇分解的形式，在一个无发散贡献和另一个无卷曲贡献中。我把惯性项写成标量势的梯度和矢量势的对偶旋度的形式。所采用的形式主义开辟了一条道路，重新制定的物质衍生物的潜力，并允许我删除虚拟力从连续介质力学。离散的运动方程，在恒定的角速度旋转不变，被用来保存每单位质量的角动量，除了每单位质量和加速度的能量守恒。这个方程中的所有变量都只用两个基本单位来表示，即长度和时间。
英文摘要：
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.
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