Note on Dirac-Born-Infeld dynamics of the D-brane near NS5-branes

In this note, we investigate the homogeneous radial dynamics of (Dp, NS5) systems without and with one compactified transverse direction, in the framework of Dirac-Born-Infeld effective action. During the homogeneous evolution, the electric field on the D-brane is always conserved and the radial motion could be reduced to a one-dimension dynamical system with an effective potential. When the Dp-brane energy is not high, the brane moves in a restricted region, with the orbits depending on the conserved energy, angular momentum through the form of the effective potential. When the Dp-brane energy is high enough, it can escape to infinity. It turns out that the conserved angular momentum plays an interesting role in the dynamics. Moreover, we discuss the gauge dynamics around the tachyon vacuum and find that the dynamics is very reminiscent of the string fluid in the rolling tachyon case.