In this chapter we present a detailed discussion on various types of oscillators, including ring and crystal oscillators. The LC resonators and integrated capacitors and inductors have been already discussed in Chapter 1, and are essential to this chapter. Furthermore, some of the communication concepts that we presented in Chapter 2, such as AM and FM signals, as well as stochastic processes, are frequently used in this chapter.

The appropriate method of data analysis depends upon a variety of factors that have been specified in the research question and as part of the research design. One key issue is whether the data are qualitative or quantitative, and this depends upon the underlying research approach. If the research approach is deductive, then most of the data are likely to be expressed as numbers and the key issue will be selecting the appropriate statistical techniques for describing and analysing the data. In this chapter, we will concentrate on techniques for describing quantitative data and for providing simple preliminary analyses.

We recall some of the basic theory of linear algebra, beginning with the formal definition of a vector space. We then discuss linear maps between vector spaces and end by proving that every vector space has a basis using Zorn’s Lemma.

We define weak convergence and give some examples, including a proof of Schur’s Theorem that weak and strong convergence coincide in l^1. We also show that closed convex subsets of Banach spaces are weakly closed. We then introduce weak-* convergence and prove two powerful weak compactness theorems: Helly’s Theorem for weak-* convergence in the duals of separable Banach spaces and a weak sequential compactness theorem in reflexive Banach spaces.

This chapter outlines the purpose, scope, and structure of the book and introduces the scientific, data-driven approach to analysing and solving business problems and conducting business research.

The primary purpose of this book is to develop methods for the dynamic analysis of multibody systems (MBS) that consist of interconnected rigid and deformable components. In that sense, the objective may be considered as a generalization of methods of structural and rigid body analysis. Many mechanical and structural systems such as vehicles, space structures, robotics, mechanisms, and aircraft consist of interconnected components that undergo large translational and rotational displacements. Figure 1.1 shows examples of such systems that can be modeled as multibody systems. In general, a multibody system is defined to be a collection of subsystems called bodies, components, or substructures. The motion of the subsystems is kinematically constrained because of different types of joints, and each subsystem or component may undergo large translations and rotational displacements.

In this chapter, approximation methods are used to formulate a finite set of dynamic equations of motion of multibody systems that contain interconnected deformable bodies. As shown in Chapter 3, the dynamic equations of motion of the rigid bodies in the multibody system can be defined in terms of the mass of the body, the inertia tensor, and the generalized forces acting on the body. On the other hand, the dynamic formulation of the system equations of motion of linear structural systems requires the definition of the system mass and stiffness matrices as well as the vector of generalized forces. In this chapter, the formulation of the equations of motion of deformable bodies that undergo large translational and rotational displacements are developed using the floating frame of reference (FFR) formulation. It will be shown that the equations of motion of such systems can be written in terms of a set of inertia shape integrals in addition to the mass of the body, the inertia tensor, and the generalized forces that appear in the dynamic formulation of rigid body system equations of motion and the mass and stiffness matrices and the vector of generalized forces that appear in the dynamic equations of linear structural systems. These inertia shape integrals that depend on the assumed displacement field appear in the nonlinear terms that represent the inertia coupling between the reference motion and the elastic deformation of the body. It will be also shown that the deformable body inertia tensor depends on the elastic deformation of the body, and accordingly it is an implicit function of time.

This chapter provides explanations of some of the fundamental issues addressed in this book. It also provides detailed derivations of some of the important equations presented in previous chapters. The first two sections of this chapter show the detailed derivation of the quadratic velocity centrifugal and Coriolis force vector of the spatial flexible body presented in Chapter 5. The final expression of these forces is obtained using two different approaches; the kinetic energy and the virtual work. It is also shown in Section 3 of this chapter how a general expression of these forces that is applicable to any set of orientation parameters can be obtained. This is the expression used in the generalized Newton–Euler equations presented in Chapter 5 of the book. The generalized centrifugal and Coriolis inertia forces associated with any set of orientation parameters including Euler angles can be obtained from the forces that appear in the Newton–Euler equations using a simple velocity transformation.

Thus far, only the dynamics of multibody systems consisting of interconnected rigid bodies has been discussed. In Chapter 2, methods for the kinematic analysis of the rigid frames of reference were presented and many useful kinematic relationships and identities were developed. These kinematic equations were used in Chapter 3 to develop general formulations for the dynamic differential equations of motion of multi-rigid-body systems. In rigid body dynamics, it is assumed that the distance between two arbitrary points on the body remains constant. This implies that when a force is applied to any point on the rigid body, the resultant stresses set every other point in motion instantaneously, and as shown in the preceding chapter, the force can be considered as producing a linear acceleration for the whole body together with an angular acceleration about its center of mass. The dynamic motion of the body, in this case, can be described using Newton–Euler equations, developed in the preceding chapter.