---
abstract: 'Stationary rotating strings can be viewed as geodesic motions in appropriate metrics on a two-dimensional space. We obtain all solutions describing stationary rotating strings in flat spacetime as an application. These rotating strings have infinite length with various wiggly shapes. Averaged value of the string energy, the angular momentum and the linear momentum along the string are discussed.'
author:
- 'Kouji Ogawa[^1], Hideki Ishihara[^2], Hiroshi Kozaki$^{1}$ Hiroyuki Nakano$^2$, and Shinya Saito[^3]'
date:  
title:  Stationary Rotating Strings as Relativistic Particle Mechanics 
---

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Introduction
============

Cosmic strings are topological defects produced by U(1) symmetry breaking in the unified field theories, which is believed to occur in the early stage of the universe[@Kibble76]. (See also [@VandS] for a review.) Verification of the existence of cosmic strings is a strong evidence of the occurrence of vacuum phase transition in the universe. For detection of the cosmic strings, clarification of the string motion is an important task.

For the cosmic strings in the framework of gauge theories, the reconnection probability is essentially one[@Shellard]. When strings cross, they reconnect and reduce their total length. The closed loops are produced by self-intersections of long strings, and loops decay through gravitational radiation. It 