The concepts of conservation and relativity lie at the heart of classical mechanics. In the hands of Descartes, Galileo, and Huygens, these concepts led to early results which were critical to its early development. However, over the following two centuries, their perceived importance to the struc- ture of mechanics underwent considerable change. In view of this complex historical development, to what extent do conservation and relativity determine the structure of mechanics? In this paper, we address this question by deriving classical mechanics—both nonrelativistic and relativistic—using relativity and conservation as the primary guiding principles. The derivation proceeds in three distinct steps. First, conservation and relativity are used to derive the asymptotically conserved quantities of motion. Second, in order that energy and momentum be continuously conserved, the mechanical system is embedded in a larger energetic framework containing a massless component that is capable of bearing energy (as well as momentum in the relativistic case). Imposition of conservation and relativity then results, in the nonrelativistic case, in the conservation of mass and in the frame-invariance of massless energy; and, in the relativistic case, in the rules for transforming massless energy and momentum between frames. Third, a force framework for handling continu- ously interacting particles is established, wherein Newton’s second law is derived on the basis of relativity and a staccato model of motion-change. Finally, in light of the derivation, we elucidate the structure of mechanics by classifying the principles and assumptions that have been employed according to their explanatory role, distinguishing between symmetry principles and other types of principles (such as compositional principles) that are needed to build up the theoretical edifice.

中文翻译：

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通过守恒和相对论推导能量框架中的经典力学

守恒和相对性的概念是经典力学的核心。在笛卡尔、伽利略和惠更斯的手中，这些概念产生了对其早期发展至关重要的早期结果。然而，在接下来的两个世纪里，它们对力学结构的重要性的认知发生了相当大的变化。鉴于这种复杂的历史发展，守恒和相对论在多大程度上决定了力学的结构？在本文中，我们通过使用相对论和守恒作为主要指导原则推导经典力学（非相对论和相对论）来解决这个问题。推导分三个不同的步骤进行。首先，守恒和相对论被用来推导出渐近守恒的运动量。第二，为了使能量和动量持续守恒，机械系统被嵌入一个更大的能量框架中，该框架包含一个能够承受能量（以及相对论情况下的动量）的无质量组件。在非相对论的情况下，守恒和相对论的强加导致质量守恒和无质量能量的框架不变性；并且，在相对论的情况下，在框架之间转换无质量能量和动量的规则中。第三，建立了处理连续相互作用粒子的力框架，其中牛顿第二定律是基于相对论和运动变化的断断续续模型推导出来的。最后，根据推导，