The previous chapter focused on describing and understanding the variability of angular momentum. We now apply those concepts to relate the motion of a system to the forces driving that motion. The formulation is based on the linear and angular momentum principles of Newton and Euler. These principles govern the motion of a single rigid body, but practical applications feature many bodies. In such situations, individual equations of motion may be written for each body. If one pursues such an analysis, careful attention must be given to accounting for the forces exerted between bodies, so the construction of free-body diagrams will play a prominent role in this chapter s development. As a supplement to this approach, a following section develops a momentum-based concept for systems of rigid bodies that sometimes can lead to the desired solution without considering all of the interaction forces. Ultimately, the energy-based concepts associated with Lagrange, whose development is taken up in the next chapter, provide a more robust alternative approach. However, they are mathematical in nature and afford little physical insight. For this reason, particular attention is given here to providing physical explanations for the results derived from the Newton Euler formulation of equations of motion.

6.1 FUNDAMENTAL EQUATIONS

6.1.1 Basic Considerations

The basic laws governing each rigid body in a system are Eq. (5.1.13) for the resultant force and Eq. (5.1.22) for the resultant moment, which are repeated here as a single reference:

It cannot be emphasized too much that this moment equation should be applied...