定义三维加速度和惯性质量导出相对论运动方程的简单形式F= MA
Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation
摘要：
牛顿第二动力学定律是一个运动定律，但也是一个有用的定义力（F=MA）或惯性质量（M=F/A），假设一个定义的加速度和平行的力和加速度。在狭义相对论中，这三种描述中只有力的描述（F=dp/dt）没有引起怀疑。最大的问题是由质量引起的，它可能是不变的静止质量或相对论质量，甚至是像纵向质量这样的方向质量。这是由于打破了力与标准加速度平行的假设。事实证明，如果相对论加速度A被定义为相对论速度减法公式，这些问题就消失了。这一基本事实被与相对论性速度微分计算有关的一些微妙之处所掩盖。它是基于力的方向，而不是基于向静止系统的转化。对非静止系统的引用产生了（看似）不同的速度减法公式。因此，相对论三维加速度既不是静止加速度，也不是四维加速度，也不是标准加速度。因此，在力的任何方向上的惯性质量与相对论质量具有相同的值。也就是说，统一了依赖于速度的横向质量和纵向质量的概念。在这项工作中，一个完整的相对论方程推导出的运动与变质量的身体，其形式证实了以前介绍的定义。此外，这些定义符合质能等效原理的一般版本。这项工作提出了一个详细的审查和讨论的不同方法的主题有关的原始历史和当代文本。在此基础上，提出了与速度变化有关的相对论性量的统一定义。
英文摘要：
Newton second law of dynamics is a law of motion but also a useful definition of force (F=MA) or inertial mass (M=F/A), assuming a definition of acceleration and parallelism of force and acceleration. In the special theory of relativity, out of these three only the description of force (F=dp/dt) does not raise doubts. The greatest problems are posed by mass, which may be invariant rest mass or relativistic mass or even directional mass like longitudinal mass. This results from breaking the assumption of parallelism of force and standard acceleration. It turns out that these issues disappear if the relativistic acceleration A is defined as a relativistic velocity subtraction formula. This basic fact is obscured by some subtlety related to the calculation of the relativistic differential of velocity. It is based on the direction of force rather than on transformation to a resting system. The reference to a non-resting system generates a (seemingly) different velocity subtraction formula. Thus, the relativistic three-dimensional acceleration is neither rest acceleration, nor four-acceleration, nor standard acceleration. As a consequence, inertial mass in any direction of the force has the same value as relativistic mass. In other words, the concepts of transverse mass and longitudinal mass, which depend on velocity, have been unified. In this work a full relativistic equation is derived for the motion of a body with variable mass whose form confirmed the previously introduced definitions. In addition, these definitions are in line with the general version of the principle of mass and energy equivalence. The work presents a detailed review and discussion of different approaches to the subject in relation to original historical and contemporary texts. On this basis, a proposal is made for consistent definition of relativistic quantities associated with velocity change.
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