Introduction to and Andy Ruina and Rudra Pratap

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Backspace CE C Chapter 0. Preface 0.1. To the student (please read) 17 d D 1 2 at 2 when you want to find t from a and d, and ax 2 C bx C c D 0 when you want to find x from a; b; and c. Once you have got this far the only problem is math 4 . Here are two tricks of the mind 1) You know a math and computer genius. She is helpful but doesn’t know any mechanics. Make your first task writing things down so she could finish up for you. She doesn’t want to help Then realize that finishing up without her is a separate job for you. You will do this later when you wear your math-genius cap. 2) Be an egotist. Pretend you are omniscient and know everything. Then write down true statements about those things; equations that contain terms that omniscient-you already know: “If I knew x; y and z the following equation would be true.” Then relax your ego a bit. Count equations and unknowns to see if you, or at least your math genius friend, could solve for the things you previously pretended to know. 4 For this and other courses, you should be good at solving math problems with your pencil and with a computer. But you should distinguish between the task of setting up a math problem and the solving of the problem. The solving often takes the bulk of the time and paper, but it’s not where your thoughts should start. The material that is new for you in this book is largely about setting up, rather than solving, the math problems that arrise in mechanics. Vectors and free-body diagrams In the toolbox of someone who can solve lots of mechanics problems are two well-worn tools: A vector calculator that always keeps vectors and scalars distinct, and A reliable and clear free-body diagram drawing tool. Because many of the terms in mechanics equations are vectors, the ability to do vector calculations is essential. Because the concept of an isolated system is at the core of mechanics, every mechanics practitioner needs the ability to draw a good free-body diagram. The second and third chapters will help you build your own set of these two most-important tools. Outside the books Guarantee: If you learn to do clear correct vector algebra and to draw good free-body diagrams you will do well at mechanics. (Assuming, of course, that you don’t totally stop studying then and there.) Statics Engineering 254 Math The books Thinking outside the books We do mechanics because we like mechanics. We hope you will too. It’s fun to puzzle out how things work. Its satisfying to do calculations that make realistic predictions. Mechanics is interesting in its own right and it feels good to take pride in new skills. We wrote this book because we want to help you learn the subject if you are interested, and get through it if you must. But we don’t know a straightforward path through your resources (say a path with 4 straight segments) that really gets you to deeper understanding. Filename:tfigure-outsidethebooks Dynamics Figure 0.1: Thinking outside of the books. A famous puzzle asks: using 4 contiguous straightline segments connect all 9 dots that are in a square 3 ¢ 3 array. The only solution has segments extending outside the “box” of 9 points. Hence the expression “thinking outside of the box”.
18 Chapter 0. Preface 0.2. A note on computation We do know that you need to think outside of the confines of your usual study resources. Like when you are relaxed, away from the pressures of books, notes, pencils or paper, say when you are walking, showering or lying down. These are the places where you naturally work out life problems, but they are good places to work out mechanics problems too. Having an animated mechanics discussion with friends is also good. You should enjoy your inner nerd socially. Are your friends turned off by techtalk There are billions of people out there, you should be able to find one or two that like to talk shop. 0.2 A note on computation Mechanics is a physical subject. The concepts in mechanics do not depend on computers. But mechanics is also a quantitative subject; relevant amounts (of length, mass, force, moment, time, etc) are described with numbers, and relations are described using equations and formulas. Computers are very good with numbers and formulas. Thus the modern practice of engineering mechanics uses computers. The most-needed computer skills for mechanics are: solution of simultaneous linear algebraic equations, plotting, and numerical solution of ODEs (Ordinary Differential Equations). More basically, an engineer also needs the ability to routinely evaluate standard functions (x 3 , cos 1 , etc.), to enter and manipulate lists and arrays of numbers, and to write short programs. Classical languages, applied packages, and simulators Programming in standard languages such as Fortran, Basic, Pascal, C++, or Java probably take too much time to use in solving simple mechanics problems. Thus an engineer needs to learn to use one or another widely available computational package (e.g., MATLAB, O-MATRIX, SCI-LAB, OC- TAVE, MAPLE, MATHEMATICA, MATHCAD, TKSOLVER, LABVIEW, etc). We assume that students have learned, or are learning such a package. Although none of the homework here depends on such, we also encourage you to play with packaged mechanics simulators (e.g., INVENTOR, WORKING MODEL, ADAMS, DADS, ODE, etc) for testing and building your intuition. How we explain computation in this book. Solving a mechanics problem involves 1. Reducing a physical problem to a well posed mathematical problem; 2. Solving the math problem using some combination of pencil and paper and numerical computation; and
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