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'.