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Engineering Dynamics

A Primer

verfasst von: Prof. Oliver M. O'Reilly

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This primer is intended to provide the theoretical background for the standard undergraduate, mechanical engineering course in dynamics. Representative problems are discussed and simulated throughout the book to illustrate fundamental concepts and explore the development of mathematical models for mechanical systems. The text grew out of the author’s desire to provide a complement to traditional texts on the subject and promote a systematic approach to problem solving. For all the examples discussed in the primer, a systematic four-step approach is employed. The third edition of the text has been revised in response to student comments on earlier editions and the increased availability of simulation software. The revisions include the addition of several new examples of models for the dynamics of systems ranging from an aerosol spray to a spherical robot. The primer has three intended audiences: undergraduate students enrolled in an introductory course on engineering dynamics, graduate students who are interesting in refreshing their knowledge, and instructors.

Review of Second Edition:
"The book is carefully written and provides a good introduction to the subject. The main objective of this primer is to reduce the gap between the theoretical framework and an undergraduate student’s ability to solve typical problems of undergraduate dynamics. Well-selected problems illustrate a systematic four-step methodology for solving problems from the dynamics of single particles, of systems of particles, of a single rigid body, and of a system of particles and rigid bodies. … At the end of each chapter some illustrative examples were added."
- Franz Selig, Zentralblatt MATH, Vol. 1201, 2011

Inhaltsverzeichnis

Frontmatter

Dynamics of a Single Particle

Frontmatter

Chapter 1. Elementary Particle Dynamics

Abstract

In this first chapter, we cover the basics on kinematics and kinetics of particles with particular emphasis on the Cartesian coordinate system. Euler’s first law (also known as Newton’s second law or the balance of linear momentum) is used to relate the kinematics of the particle to the forces acting on it. This law provides a set of differential equations for the motion of the particle. We illuminate the developments using three ubiquitous examples involving projectile motion both in the presence and absence of drag forces. Our treatment of dynamics makes extensive use of vector calculus. For the interested student, a summary of the needed results from vector calculus is presented in Appendix A.

Oliver M. O’Reilly

Chapter 2. Particles and Cylindrical Polar Coordinates

Abstract

In this chapter, we discuss the cylindrical polar coordinate system and how it can be used in particle mechanics. This coordinate system and its associated basis vectors find application in a range of problems including particles moving on circular arcs and helical curves. To illustrate applications of the cylindrical polar coordinate system to particle mechanics, two examples involving planar pendula are discussed and a qualitative discussion of some aspects of their dynamics is presented.

Oliver M. O’Reilly

Chapter 3. Particles and Space Curves

Abstract

We discuss the differential geometry of space curves (a curve embedded in Euclidean three-space) in this chapter. In particular, we introduce the Serret-Frenet basis vectors. This is followed by the derivation of an elegant set of relations describing the rate of change of the unit tangent, unit principal normal, and unit binormal vectors. Several examples of space curves are then discussed. We end the chapter with several applications to the mechanics of particles. Subsequent chapters also contain discussions of several pertinent examples.

Oliver M. O’Reilly

Chapter 4. Friction Forces and Spring Forces

Abstract

Formulations of two ubiquitous forces are discussed in this chapter: friction forces and spring forces. We start with the former and consider a simple classic experiment. Based on this experiment, general (coordinate-free) expressions for friction forces are obtained. The chapter closes with the corresponding developments for a spring force. Several examples are used throughout the chapter to illustrate applications of the formulations of the spring and friction forces.

Oliver M. O’Reilly

Chapter 5. Power, Work, and Energy

Abstract

The chapter starts with a discussion of the notions of power and work. Subsequently, we make these ideas more precise by defining the mechanical power of a force and, from this, the work done by the force during the motion of a particle. Next, the work-energy theorem is derived from the balance of linear momentum. It is then appropriate to discuss conservative forces, and we spend some added time discussing the potential energies of gravitational and spring forces. With these preliminaries aside, energy conservation is discussed and a second form of the work-energy theorem is established. Numerous examples are presented that show how to prove and exploit energy conservation if it occurs in a problem featuring the dynamics of a particle.

Oliver M. O’Reilly

Dynamics of a System of Particles

Frontmatter

Chapter 6. Momenta, Impulses, and Collisions

Abstract

As a prelude to the discussion of a system of particles, the linear and angular momenta of a single particle are introduced in this chapter. In particular, conditions for the conservation of these kinematical quantities are established. This is followed by a discussion of impact problems where particles are used as models for the impacting bodies.

Oliver M. O’Reilly

Chapter 7. Dynamics of Systems of Particles

Abstract

In this chapter, we continue the process of extending several results pertaining to a single particle to a system of particles. We start by defining the linear momentum, angular momenta, and kinetic energy for a system of particles. Next, we introduce a new concept, the center of mass C of a system of particles. A discussion of the conservation of kinematical quantities follows. Conservations of energy and momenta along with energy dissipation are illustrated using several detailed examples.

Oliver M. O’Reilly

Dynamics of a Single Rigid Body

Frontmatter

Chapter 8. Planar Kinematics of Rigid Bodies

Abstract

Background material on the planar kinematics of rigid bodies is presented in this chapter. In particular, we show how to establish certain useful representations for the velocity and acceleration vectors of any material point of a rigid body. We also discuss the angular velocity vector of a rigid body. These concepts are illustrated using three important applications: mechanisms, rolling rigid bodies, and sliding rigid bodies. Finally, we discuss the linear and angular momenta of rigid bodies and the inertias that are used to relate the angular momentum of a rigid body relative to its center of mass and the angular velocity vector of the rigid body.

Oliver M. O’Reilly

Chapter 9. Kinetics of a Rigid Body

Abstract

We start by discussing Euler’s laws for a rigid body. These laws are known as the balances of linear and angular momenta. An alternative form of these laws is also presented that is useful for solving many classes of problems. We then discuss the kinetic energy of a rigid body and establish the Koenig decomposition. This decomposition, combined with the balance laws, can be used to prove a work-energy theorem for a rigid body. As illustrations of the theory, we consider four classes of problems: purely translational motion of a rigid body, rigid bodies that are free to rotate about one of their fixed material points, rolling rigid bodies and sliding rigid bodies, and an imbalanced rotor problem. These applications are far from exhaustive, but we believe they are the chief representatives of problems in an undergraduate engineering dynamics course.

Oliver M. O’Reilly

Dynamics of Systems of Particles and Rigid Bodies

Frontmatter

Chapter 10. Systems of Particles and Rigid Bodies

Abstract

This chapter is the culmination of the primer. To start, the linear momentum of a system of K particles and N rigid bodies is discussed. Similarly, the angular momenta and kinetic energy of such a system are developed. We then turn to the balance laws for a system and demonstrate how the balance laws can be used to determine the equations of motion, conservations of energy, angular momentum, and linear momentum in a range of examples. These examples include a double pendulum, a semi-circular cylinder rolling on a cart, a simple model for a spherical robot, and impact problems.

Oliver M. O’Reilly

Backmatter

Titel: Engineering Dynamics
verfasst von: Prof. Oliver M. O'Reilly
Verlag: Springer International Publishing
Electronic ISBN: 978-3-030-11745-0
Print ISBN: 978-3-030-11744-3
DOI: https://doi.org/10.1007/978-3-030-11745-0