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| 平面图形的静矩与惯性矩关系系数研究 |
| Research on Relationship Coefficient Between Static Moment and Inertia Moment of Plane Graph |
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| DOI：10.16018/j.cnki.cn32-1650/n.202204005 |
| 中文关键词: 静矩 惯性矩 静矩与惯性矩关系系数 标度变换不变性 有质平面图形 |
| 英文关键词: static moment inertia moment relationship coefficient between static moment and inertia moment scale transformation invariance qualitative plane figures |
| 基金项目: |
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| 摘要点击次数: 32 |
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| 中文摘要: |
| 为研究液体危险品道路运输的液罐半挂车上下坡时，因系统的质心位置变化，导致整车性能和侧向稳定性降低引发的翻车事故问题，以斜立式圆柱罐体系统为研究对象，结果表明罐体系统的稳度仅取决于罐内液体在坡面上投影的力学性质。引入平面图形的静矩与惯性矩关系系数，可将系统稳度的立体问题简化为平面问题。当不考虑平面质量时，系数具有标度变换不变性、定轴平移不变性以及垂直轴等值性；当质量均匀分布时，系数仍具有标度变换不变性，即无论是否进行标度变换，它的静矩与惯性矩关系系数总保持不变，且与不考虑质量时相同。 |
| 英文摘要: |
| In order to study the rollover accident caused by the decline of the vehicle performance and lateral stability due to the change of the position of the center of mass of the system when the liquid tank semi-trailer for road transport of dangerous liquid goods is going up and down the slope, the inclined cylindrical tank system is taken as the research object, and the results show that the stability of the tank system only depends on the mechanical properties of the liquid in the tank projected on the slope. By introducing the relationship coefficient between the static moment and the inertia moment of the plane figure, the three-dimensional problem of system stability can be simplified to the plane problem. When the plane mass is not considered, the coefficient has scale transformation invariance, fixed axis translation invariance and vertical axis equivalence. When the mass is uniformly distributed, the coefficient still has scale transformation invariance, that is, whether scale transformation is carried out or not, the relationship coefficient between the static moment and the inertia moment always remains unchanged, and is the same as when the mass is not considered. |
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