  Accretion disks surrounding compact objects, and other environmental factors,
deviate satellites from geodetic motion. Unfortunately, setting up the
equations of motion for such relativistic trajectories is not as simple as in
Newtonian mechanics. The principle of general (or Lorentz) covariance and the
mass-shell constraint make it difficult to parametrize physically adequate
4-forces. Here, we propose a solution to this old problem. We apply our
framework to several conservative and dissipative forces. In particular, we
propose covariant formulations for Hooke's law and the constant force, and
compute the drag due to gravitational and hard-sphere collisions in dust, gas
and radiation media. We recover and covariantly extend known forces such as
Epstein drag, Chandrasekhar's dynamical friction and Poynting-Robertson drag.
Variable-mass effects are also considered, namely Hoyle-Lyttleton accretion and
the variable-mass rocket. We conclude with two applications: 1. The
free-falling spring. We find that Hooke's law corrects the deviation equation
by an effective Anti-de Sitter tidal force; 2. Black hole infall with drag. We
numerically compute some trajectories on a Schwarzschild background supporting
a dust-like accretion disk.
