曲线几何性质和力学性质的微分表达式$f^2+f'^2$、$f+f"$和$f f"- f'^2$的相关性
On the relevance of the differential expressions $f^2+f'^2$, $f+f"$ and $f f"- f'^2$ for the geometrical and mechanical properties of curves
摘要：
我们提出了一个统一的方法，以已知的和新的性质的曲线，显示无处不在的表达式在标题中的分析处理，其机械和几何性质
英文摘要：
We present a unified approach to known and new properties of curves by showing the ubiquity of the expressions in the title in the analytic treatment of their mechanical and geometric properties
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
