Brane Mechanics

In this paper, we investigate about two physically distinct classes of the one-dimensional' worldvolume solutions describing the status of an arbitrary brane in the presence of another arbitrary (flat) brane which supplies the required supergravity background. One of these classes concerns with a relative (transverse) motion of two parallel flat branes, while the other class is related to a static configuration in which one of the branes is flat and the other is curved as a cylindrical hypersurface. Global symmetries of the worldvolume theory are used to show that both types of these solutions are described by some sort of planar orbits’ which are specified by their energy' and angular momentum’ $(E,l)$ parameters. We find that various phases of the motion' along these orbits, for different values of $(E,l)$, are easily deduced from the curve of an $E$-dependent function of the relative distance’ between the two branes, which is somehow related to their mutual `effective potential’.