Solving Engineering Problems in Dynamics by Michael B. Spektor
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Solving Engineering Problems in Dynamics by Michael B. Spektor

Purposeful control and improvement of how existing mechanical systems perform is an important real-life problem, as is the development of new systems. We can obtain solutions to these problems by investigating the working processes of machines and their units and elements. These investigations should be based on fundamentals of dynamics combined with a variety of related sciences. The working processes that characterize system performance can be described by mathematical expressions that actually represent equations of motion of these systems.

Analyzing these equations of motion reveals the relationship between the parameters of the system and their infl uence on performance and other system characteristics or elements. This book contains comprehensive methods for analyzing the motion of engineering systems and their components. The analysis covers three basic phases: 1) composing the differential equation of motion, 2) solving the differential equation of motion, and 3) analyzing the solution.

Engineering education provides the fundamental skills for completing these three phases. However, many engineers would benefi t from additional training in using these fundamentals to solve real-life engineering problems. This book provides this training by describing in a step-by-step order the methods related to each of these three phases. When assembling a differential equation of motion, it is essential to completely understand the components of this equation as well as the system’s working process. This book describes all possible components of the differential equation of motion and all possible factors of the working process.

In mechanical engineering, all these components and factors represent forces and moments. The characteristics of all these loading factors and their application to particular differential equations of motion are presented in this book. This book also introduces a straightforward universal methodology for solving differential equations of motion by using the Laplace Transform. This approach replaces calculus with conventional algebraic procedures that do not represent any diffi culties for engineers. Using the Laplace methodology to solve differential equations of motion does not require memorizing the fundamentals of the Laplace Transform.

Instead, this book presents an appropriate table of Laplace Transform pairs. It then explains how to use the pairs to convert differential equations into algebraic equations and then how to invert the solutions of these algebraic equations into conventional equations representing the functions of displacement of time. Analyzing the solutions of differential equations of motion reveals the role of the system’s parameters, the infl uence of these parameters on each other, and how to control the performance of the system. The motion of a mechanical system is characterized by its displacement, velocity, and acceleration.

These three characteristics are the three basic parameters of the system’s motion. All other characteristics of the working processes can be determined by analyzing these three parameters. The equation of motion represents the displacement of the system as a function of time. The other two parameters — velocity and acceleration — are respectively the fi rst and second derivatives from the displacement. Thus, the equation of motion is the basis for solving the mechanical engineering problem. The equations of motion represent the solutions of differential equations of motion that refl ect the real working processes of the systems.

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