Body Forces

In addition to the surface tractions, other forces act on each part of a body. These are called the body forces like the gravity force, intermolecular force. The magnitude of such forces varies proportionally with the mass of the particle on which they act and their direction depends on the position of the particles in the field of force.

If are the components of the intensity field at any point and m is the mass of a particle at that point, then are the forces of the field that act on the particle forming part of the body.

Equation of Motion

Body forces applied on any portion of the body is statically equivalent to a single force applied at one point together with a couple .
The components parallel to the axes of the single force are,

(2.3)

is the density of the body at the point and the integration is taken throughout the volume of the body.

Similarly the tractions on the elements of area of the surface of the portion of the body are equivalent to a resultant force and a couple . The components of the force are,

(2.4)

where integration is taken over the surface of the portion.

The center of mass of the portion moves like a particle under the action of these two types of forces. If are the acceleration of the particle which is located at at time t , then the equation of motion of the particle are

(2.5)

The change of moment of momentum of the portion of the body are

(2.6)