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
Four-velocity the 3d position vector, written as a column vector The components of the velocity formula_2 (tangent to the curve) at any point on the world line are Each component is simply written In Einstein's theory of relativity, the path of an object moving relative to a particular frame of reference is defined by four coordinate functions "x"("τ"), where μ is a spacetime index which takes the value 0 for the timelike component, and 1, 2, 3 for the spacelike coordinates. The zeroth component is defined as the time coordinate multiplied by "c", Each function depends on one parameter "τ" called