  A new theory for the dynamics of the magnetic particles and their magnetic
moments in ferrofluids is developed. Based on a generalized Lagrangian
formulation for the equations of motion of the colloidal particle, we introduce
its interaction with the solvent fluid via dissipative and random noise
torques, as well as the interactions between the particle and its magnetic
moment, treated as an independent physical entity and characterized by three
generalized coordinates, its two polar angles and its modulus. It has been
recognized recently that inertial effects, as well as the particle's rotational
Brownian motion, may play important roles on the dynamic susceptibility of a
class of magnetic fluids. No satisfactory theory existed, up to now, that takes
this effects into account. The theory presented here is a first-principles
3-dimensional approach, in contrast to some phenomenological 2-dimensional
approaches that can be found in the recent literature. It is appropriate for
superparamagnetic, non-superparamagnetic and mixed magnetic fluids. As a simple
application, the blocked limit (magnetic moment fixed in the particle) is
treated numerically. The rotational trajectory of the particles in presence of
a magnetic field, as well as the response functions and dynamic susceptibility
matrices are explicitly calculated for some values of the parameters
