一种基于广义刚度和广义惯性密度的量纲分析方法 / A Dimensional Analysis Method Based on Generalized Stiffness and Generalized Inertial Density

传统量纲分析方法以质量(M)、长度(L)、时间(T)为基本量纲,在物理常数拆解与跨领域波动方程比对过程中,质量与时间的基础独立性会混合恢复力属性与惯性属性,遮蔽动力学方程底层共通结构。本文提出一种基于广义刚度(K)和广义惯性密度(I)的辅助量纲分析体系,以空间尺度(L)作为第三基础量。通过引入本构约束 K=I·v²,将时间、质量等传统基础量全部视为导出量。KIL体系与MLT体系之间可互相换算,不作为MLT的替代,仅作为物理量拆解、跨领域关联性分析,统一理论构建的辅助工具。 Traditional dimensional analysis methods use mass (M), length (L), and time (T) as fundamental dimensions. This paper proposes an auxiliary dimensional analysis system based on generalized stiffness (K) and generalized inertial density (I), using spatial scale (L) as the third fundamental dimension. By introducing the constitutive constraint K=I·v², traditional fundamental dimensions such as time and mass are treated entirely as derived quantities. The KIL system and MLT system are mutually convertible; KIL is not a replacement for MLT, but serves as an auxiliary tool for physical quantity decomposition, cross-domain correlation analysis, and unified theory construction.