<p>The paper presents a theory to describe systems experiencing gravitational and electromagnetic interactions. It is formulated in a fluid dynamical framework generalized to the case where space is not necessarily Euclidean. The evolution in this theory is generated by a vector field and the dynamical equations are first order in time. The dynamical vector field is, moreover, the sum of two vector fields, a Hamiltonian vector field that is associated with the energy function, being derived using Hamilton’s principle of least action and a gradient vector field associated with a dissipation function being the gradient thereof. A model of a physical system is thus, defined by the specification of the energy function including an expression for the gravitational energy, and the dissipation function. It is to be noted that the equations of motion satisfy the integral laws of conservation of energy and momentum and the second law of thermodynamics.</p>