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

James Bell Cooper

paper

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

arXiv:1102.1579

Abstract

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

On the relevance of the differential expressions f2+f′2, f+f" and ff"−f′2 for the geometrical and mechanical properties of curves

Abstract

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