Added mass fluid quasi-momentum. Unsteady forces due to a change of the relative velocity of a body submerged in a fluid can be divided into two parts: the virtual mass effect and the Basset force. The origin of the force is that the fluid will gain kinetic energy at the expense of the work done by an accelerating submerged body. It can be shown that the virtual mass force, for a spherical particle submerged in an inviscid, incompressible fluid is where bold symbols denote vectors, formula_2 is the fluid flow velocity, formula_3 is the spherical particle velocity, formula_4 is the mass density
Rigid body dynamics the rigid body. The velocity of the points R along their trajectories are where ω is the angular velocity vector of the body. Work is computed from the dot product of each force with the displacement of its point of contact If the trajectory of a rigid body is defined by a set of generalized coordinates "q", "j" = 1, ..., "m", then the virtual displacements δr are given by The virtual work of this system of forces acting on the body in terms of the generalized coordinates becomes or collecting the coefficients of δq For simplicity consider a trajectory