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Equations of Motion Written With Respect to the Reference Configuration. 201

4.11 Equations of Motion Written With Respect to the Reference Configuration,
In this section, we shall show that with respect to the reference configuration, the equations
of motion can be written as follows:

where (T 0)ij are the Cartesian components of the first Piola-Kirchhoff stress tensor, p 0 is the
density in the reference configuration, Xj are the material coordinates and B/ and a/ are
body force per unit mass and the acceleration components respectively.
From Eq. (4.10.7b), we have

Thus,

j
Now,

and we can show that the last term of Eq. (ii) is zero as follows:

t In Chapter 7, an alternate shorter proof will be given.