Straight rotating string with one fixed endpoint
= Straight rotating string with one fixed endpoint
{title2=$\omega L=1$}
A <Nambu–Goto action> solution with $X^0=t$ is $\boldsymbol X=L\sin(\sigma/L)(\cos(t/L),\sin(t/L))$, for $0\leq\sigma\leq\pi L/2$. It solves the <wave equation>, has a fixed endpoint at the origin, and obeys the <free-end string boundary condition> at the other end. Its <proper length> is $L$ and its free endpoint has angular speed $1/L$ and spatial speed one.