  We discuss a micro-swimmer model made of three spheres actuated by an
internal active time-periodic force, tied by an elastic potential and submitted
to hydrodynamic interactions with thermal noise. The dynamical approach we use,
replacing the more common kinetic one, unveils the instability of the original
model and the need of a confining potential to prevent the evaporation of the
swimmer. We investigate the effect of the main parameters of the model, such as
the frequency and phase difference of the periodic active force, the stiffness
of the confining potential, the length of the swimmer and the temperature and
viscosity of the fluid. Our observables of interest are the averages of the
swim velocity, of the energy consumption rate, the diffusion coefficient and
the swimming precision, which is limited by the energy consumption through the
celebrated Thermodynamic Uncertainty Relations. An optimum for velocity and
precision is found for an intermediate frequency. Reducing the potential
stiffness, the viscosity or the length, is also beneficial for the swimming
performance, but these parameters are limited by the consistency of the model.
Analytical approximation for many of the interesting observables is obtained
for small deformations of the swimmer. We also discuss the efficiency of the
swimmer in terms of its maximum precision and of the hydrodynamic, or
Lighthill, criterion, and how they are connected.
