Mathematical Modeling of Mechanical Systems

Abstract

In this chapter, the modeling of translational and rotational mechanical and elctromechanical systems is presented. Differential equation models are first derived, and then the corresponding transform model is used for easier analysis of systems. The initial conditions are included in the analysis. Furthermore, the electrical analog of mechanical systems is used to further simplify the analysis. The topology of a network is the way the various components of a system are interconnected. The analogy that preserves the topologies of the network of different systems those can be transformed with a one-to-one correspondence that is continuous in both directions is used. As voltage and velocity are across variables and current and force are through variables, the topology of the systems remains the same using this analogy. The input–output relationships of basic circuit elements, mass, spring, and dashpot are given. Newton’s law governs the behavior of mechanical systems, which states that the algebraic sum of forces on a rigid body in a given direction is equal to the product of the mass of the body and its acceleration in the same direction. For rotational systems, the algebraic sum of torques about a fixed axis is equal to the product of the inertia and the angular acceleration about the axis is the version of Newton’s second law of motion. Emphasis on physical simulation of systems is a unique feature, making it easier to understand system behavior.