TABLE OF CONTENTS This chapter demonstrated the principles involved in developing simplified lumpedparameter mathematical models of mechanical systems of two basic types: (a) translational systems and (b) rotational systems. In each case, the system model was developed through the use of Newton s laws dealing with summation of forces at a massless point (or torques at an inertialess point) and acceleration of a lumped mass (or lumped inertia), together with elemental equations for springs, dampers, or both. When carried out properly, this results in a set of n equations containing n unknown variables. Subsequent mathematical manipulation of these equations was carried out to eliminate unwanted variables, producing the desired model involving the variables of greatest interest.
Usually, this desired model consisted of a single input-output differential equation relating a desired output to one or more given inputs. In some cases, a reduced set of first-order equations, called state-variable equations, was developed as part of the process of eliminating unwanted variables. This was done because, in some instances in the future, this is all the reduction needed to proceed with a computer simulation or analysis of the system. The definition of state variables is left to Chap. 3, which covers the topic of this aspect of system modeling in considerable detail.
The energy converters required for coupling translational with rotational systems are discussed in Chap. 10, in which the general topic of energy converters in mixed systems is covered in some detail.
During the development of this chapter, the basic...
