  We explore the dynamical signatures imprinted by baryons on dark matter
haloes during the formation process using the OverWhelmingly Large Simulations
(OWLS), a set of state-of-the-art high-resolution cosmological hydrodynamical
simulations. We present a detailed study of the effects of the implemented
feedback prescriptions on the orbits of dark matter particles, stellar
particles and subhaloes, analysing runs with no feedback, with stellar feedback
and with feedback from supermassive black holes. We focus on the central
regions (0.25 r_{200}) of haloes with virial masses ~ 6 x 10^{13} (~ 7 x
10^{11}) Msun/h at z = 0(2). We also investigate how the orbital content
(relative fractions of the different orbital types) of these haloes depends on
several key parameters such as their mass, redshift and dynamical state. The
results of spectral analyses of the orbital content of these simulations are
compared, and the change in fraction of box, tube and irregular orbits is
quantified. Box orbits are found to dominate the orbital structure of dark
matter haloes in cosmological simulations. There is a strong anticorrelation
between the fraction of box orbits and the central baryon fraction. While
radiative cooling acts to reduce the fraction of box orbits, strong feedback
implementations result in a similar orbital distribution to that of the dark
matter only case. The orbital content described by the stellar particles is
found to be remarkably similar to that drawn from the orbits of dark matter
particles, suggesting that either they have forgotten their dynamical history,
or that subhaloes bringing in stars are not biased significantly with respect
to the main distribution. The orbital content of the subhaloes is in broad
agreement with that seen in the outer regions of the particle distributions.
