has been shown that the stationary rotating strings with an angular velocity $\Omega$ are described by geodesics in two-dimensional curved spaces with positive definite metrics with a parameter, $q$ in this paper. The metrics admit a Killing vector which generates rotation symmetry, then the geodesics in the two-dimensional spaces have a constant of motion, $\ell$ in this paper. Therefore, the stationary rotating strings in Minkowski spacetime are characterized by three parameters $(\Omega, q, \ell)$.

One of the typical stationary rotating strings are the , $|q|+|\ell|=1$, where a snapshot looks a helix. The world surface of the helical string is the two-dimensional homogeneous space embedded in Minkowski spacetime. For general $(\Omega,q,\ell)$, stationary rotating strings have quasi-periodic structure along the rotation axis. Only in the case of rational $\ell$, the strings have exact periodicity. The strings display much variation in the shape which depends on $q$ and $\ell$.

We have obtained the following averaged values per unit length along the rotation axis: energy, angular momentum and linear momentum along the axis. It should be noted that the rotation of the strings around the axis induces the linear momentum along the axis because of the inclination of string segments.

By the advantage of 