  The phase space of a classical particle in DSR contains de Sitter space as
the space of momenta. We start from the standard relativistic particle in five
dimensions with an extra constraint and reduce it to four dimensional DSR by
imposing appropriate gauge fixing. We analyze some physical properties of the
resulting theories like the equations of motion, the form of Lorentz
transformations and the issue of velocity. We also address the problem of the
origin and interpretation of different bases in DSR.
