Motion of the continuum
A set of three figures showing the deformation at time t= 0, t
1 and t2The same body deforms with time under the action of external forces. The
point P embedded in the volume element 
traverses a path called the trajectory. This path is described by the
displacement function 
is
continuous within the space and time. Thus
can be defined. Note that if the function
is not continuous, then the derivatives cannot even be defined.