Mass and Moment Line Integrals

Expanding on the concept of Line Integrals, coil springs and wires are treated as masses distributed along smooth curves in space. In this file we are considering parametrized curves $C=r(g(t),h(t),k(t))$

• Density is given by $\delta (x,y,z)$ and $\delta (x(t),y(t),z(t))$ in parametrized circumstances
• The arc differential becomes $ds=\sqrt{((x^{\prime }(t){)}^2,(y^{\prime }(t{)}^2,(x^{\prime }(t){)}^2}dt$

The formula for mass along a Curve $C$

$$M=\int \_a^b\delta (x(t),y(t),z(t))ds$$