A new scaling theory called finite similitude has appeared in the open literature for the scaling of physical systems. The theory is founded on the metaphysical concept of and consequently can in principle be applied to all physics. With regard to the application of the theory to multi-physics however, an obstacle is dissimilar mathematical formulations, that are preferred and applied in practice. This paper looks to combine electrical and mechanical physics under the rules of the scaling theory for the analysis of scaled electromechanical systems. To facilitate this the physics of electromechanics is described using transport equations on a projected space termed the scaling space. It is shown that this approach unifies the mechanical and electrical descriptions and allows the scaling theory to be applied and for scaling identities to be established. Additionally, on confirming that the scaling space possesses all the attributes of a real physical space (despite being a mere projection), mathematical modelling (to great advantage) is performed directly and integrated with the scaling theory. To showcase the concepts, mathematical models for previously researched electromechanical systems are directly analysed in the new scaling space. It is demonstrated how such models automatically account for scale dependencies in the electromechanical systems they represent. The huge potential of the new approach is revealed providing the means for formulating (for the first time) realistic representative scaled-mathematical models.

中文翻译：

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比例机电理论


一种称为有限相似的新标度理论已经出现在用于物理系统标度的开放文献中。该理论建立在形而上学概念的基础上，因此原则上可以应用于所有物理学。然而，就该理论在多物理场的应用而言，一个障碍是不同的数学公式，而这些数学公式在实践中是首选和应用的。本文着眼于在标度理论规则下结合电气和机械物理来分析标度机电系统。为了促进这一点，机电物理学是使用称为缩放空间的投影空间上的传输方程来描述的。结果表明，这种方法统一了机械和电气描述，并允许应用缩放理论并建立缩放恒等式。此外，在确认缩放空间拥有真实物理空间的所有属性（尽管只是投影）后，直接进行数学建模（具有很大的优势）并与缩放理论相结合。为了展示这些概念，在新的缩放空间中直接分析先前研究的机电系统的数学模型。演示了此类模型如何自动考虑它们所代表的机电系统中的尺度依赖性。新方法的巨大潜力被揭示，提供了（首次）制定现实的代表性比例数学模型的方法。