  In this work, we investigate the rotational dynamics of the ginger-shaped
near-Earth asteroid 4179 Toutatis, which was closely observed by Chang'e-2 at a
distance of $770\pm120~$ meters from the asteroid's surface during the outbound
flyby \citep{Huang2013} on 13 December 2012. A sequence of high-resolution
images was acquired during the flyby mission. In combination with ground-based
radar observations collected over the last two decades, we analyze these flyby
images and determine the orientation of the asteroid at the flyby epoch. The
3-1-3 Euler angles of the conversion matrix from the J2000 ecliptic coordinate
system to the body-fixed frame are evaluated to be $-20.1^\circ\pm1^\circ$,
$27.6^\circ\pm1^\circ$ and $42.2^\circ\pm1^\circ$, respectively. The
least-squares method is utilized to determine the rotational parameters and
spin state of Toutatis. The characteristics of the spin-state parameters and
angular momentum variations are extensively studied using numerical
simulations, which confirm those reported by \citet{Takahashi2013}. The large
amplitude of Toutatis' precession is assumed to be responsible for its tumbling
attitude as observed from Earth. Toutatis' angular momentum orientation is
determined to be described by $\lambda_{H}=180.2^{+0.2^\circ}_{-0.3^\circ}$ and
$\beta_{H}=-54.75^{+0.15^\circ}_{-0.10^\circ}$, implying that it has remained
nearly unchanged for two decades. Furthermore, using Fourier analysis to
explore the change in the orientation of Toutatis' axes, we reveal that the two
rotational periods are 5.38 and 7.40 days, respectively, consistent with the
results of the former investigation. Hence, our investigation provides a clear
understanding of the state of the rotational dynamics of Toutatis.
