Page 95 - Introduction to Continuum Mechanics

80 Kinematics of a Continuum

the path lines of every particle in a continuum can be described by a vector equation of the

Fig. 3.1

form

e +JC e
where x = x^i +*2 2 3 3 * s tne position vector at time t for the particle P which was at
X = X&i+X&z+XTto (see Fig. F3.1).
In component form, Eq. (3.1.1) takes the form:

or

In Eqs. (3.1.2), the triple (ATj^X^s) serves to identify the different particles of the body
and is known as material coordinates. Equation (3.1.1) or Eqs. (3.1.2) is said to define a
motion for a continuum; these equations describe the pathline for every particle in the
continuum. They may also be called the kinematic equations of motion.

Example 3.1.1

Consider the motion