  The interaction of light with short light pulses is relevant in optical
traps, optical tweezers, and many other applications. The theoretical
description of such polychromatic light-matter interaction is challenging, and
more so when the object is moving with respect to the light source, albeit with
constant speed. Light sails are futuristic examples where such speed should
reach the relativistic regime. In here, we provide a methodology for the
theoretical and numerical analysis of the interaction of light pulses with
objects moving with constant speed. The methodology allows one, in particular,
to readily compute the transfer of fundamental quantities such as energy and
momentum from the light pulse to the object. As an example, we compute the
transfer of energy and momentum between a given pulse and a silicon sphere
moving at relativistic speeds. The methodology, however, is valid for generic
pulses and objects. Particularizing the equations to the case of zero speed
allows one to treat static or quasi-static objects. The method is based on the
polychromatic T-matrix formalism, which leverages the many publicly available
resources for computing T-matrices.
