The Field of Motion and the Equation of Continuity The Field of
Motion. Among vector fields the field of motion is of special
importance. Several of the characteristics of the field of
motion can be dealt with without considering the forces which
have brought about or which maintain the motion, and these
characteristics form the subject of kinematics. The velocity of
a particle relative to a given coordinate system is defined as ν
= dr/dt, where dr is an element of length in the direction in
which the particle moves. In a rectangular coordinate system the
velocity has the components The velocity field can be completely
described by the Lagrange or by the Euler method. In the
Lagrange method the coordinates of all moving particles are
represented as functions of time and of a threefold multitude of
parameters that together characterize all the moving particles.
From this representation the velocity of each particle, and,
thus, the velocity field, can be derived at any time. The more
convenient method by Euler