observations in our Galaxy. For example, the age-velocity dispersion relation of stars in the solar neighborhood [e.g., @Holmberg+2007] most naturally accounts for the existence of the non-steady spirals [@CarlbergSellwood1985; @BinneyLacey1988; @JenkinsBinney1990; @deSimone+2004]. @Baba+2009 analyzed the kinematics of star-forming regions using numerical simulation data of a barred galaxy such as the Milky Way galaxy [@Baba+2010], and they found that the kinematics of these regions are consistent with the observed peculiar motions of maser sources. These studies support the view that the Galactic stellar spiral arms are non-steady instead of stationary density waves.

However, the current theoretical understanding of the dynamics of non-steady spirals is thus far insufficient. It has been suggested that a key factor towards understanding their dynamics is the orbital evolution of stars. In this study, we analyze the orbits of stars associated with non-steady spirals in the growth and damping phases.

In Section \[sec:Method\], we summarize the numerical model and the method, which are the same as reported by @Wada+2011, except that the present model does not include the ISM, i.e., our study involves pure $N$-body simulations. We examine the global evolution of the stellar disk in Section \[sec:GlobalMorphology\], in which we show the non-steady nature of spirals 