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Über dieses Buch

This engineering dynamics textbook is aimed at beginning graduate students in mechanical engineering and other related engineering disciplines who need training in dynamics as applied to engineering mechanisms. It introduces the formal mathematical development of Lagrangian mechanics (and its corollaries), while solving numerous engineering applications. The author’s goal is to instill an understanding of the basic physics required for engineering dynamics, while providing a recipe (algorithm) for the simulation of engineering mechanisms such as robots. The book will be reasonably self-contained so that the practicing engineer interested in this area can also make use of it. This book is made accessible to the widest possible audience by numerous, solved examples and diagrams that apply the principles to real engineering applications.

• Provides an applied textbook for intermediate/advanced engineering dynamics courses;
• Discusses Lagrangian mechanics in the context of numerous engineering applications;
• Includes numerous, solved examples, illustrative diagrams and applied exercises in every chapter

Inhaltsverzeichnis

Frontmatter

1. Particle Mechanics

Abstract
In which we go from Newton’s second law for a particle to the Euler-Lagrange equations including “viscous” dissipation with a brief digression to discuss rotating coordinate systems…
Roger F. Gans

2. Rigid Body Mechanics

Abstract
In which we find that a rigid body has six degrees of freedom, learn how to describe the orientation of a rigid body in terms of Euler angles, define inertial and body coordinates and find the Euler-Lagrange equations for a single rigid body…
Roger F. Gans

3. Forces and Constraints

Abstract
In which we say something about generalized forces and discuss constraints and how to apply them, introduce Lagrange multipliers for common nonholonomic constraints and take a quick look at one-sided constraints…
Roger F. Gans

4. Alternate Formulations

Abstract
In which we learn about several alternate formulations based on the Lagrangian: Hamilton’s equations, the method of quasicoordinates and a neat way to eliminate Lagrange multipliers from many nonholonomically constrained problems…
Roger F. Gans

5. Kane’s Method and the Kane-Hamilton Synthesis

Abstract
In which we develop Kane’s method following the original work and introduce a modification of Hamilton’s equations that takes advantage of some of the tricks of the trade introduced by Kane & Levinson…
Roger F. Gans

6. Simple Motors, Stability and Control

Abstract
In which we explore a number of topics that we need for real engineering problems…
Roger F. Gans

7. Mechanisms and Robots

Abstract
In which we apply the fundamentals to some model problems closer to reality than we have seen so far….
Roger F. Gans

8. Wheeled Vehicles

Abstract
In which we look at various wheeled vehicles, both for their own sake, and as models for more complicated wheeled systems (such as the bicycle model for a car)…
Roger F. Gans

9. Appendix A: Indicial Notation

Abstract
Lagrangian dynamics and the various variants in use (Hamilton’s equations, Kane’s equations, the method of quasicoordinates and the Kane-Hamilton synthesis introduced in this text) use abstract vector spaces (for example configuration space and state space). These are K dimensional vector spaces with length defined as the square root of the dot product of a vector with itself. Two vectors are perpendicular (or orthogonal) if their dot product is zero. The dot product is defined as one would expect by analogy to the dot product for ordinary vectors: the product of the first pair of components, plus the product of the second pair of components and so on out until all K pairs of components have been multiplied and added. Ordinary vector notation, either classical or in the context of linear algebra does not suffice for everything one wants to do, so I will introduce an indicial notation closely related to that of tensor analysis. It will not be tensor analysis, but the reader familiar with tensors will find much that is familiar in this appendix.
Roger F. Gans

Backmatter

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