A Conceptual Glossary for Systems Engineering: Define the Concept, Don't Quibble About the Terms
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Analysis of Functions of a Single Variable a Detailed Development
ANALYSIS OF FUNCTIONS OF A SINGLE VARIABLE A DETAILED DEVELOPMENT LAWRENCE W. BAGGETT University of Colorado OCTOBER 29, 2006 2 For Christy My Light i PREFACE I have written this book primarily for serious and talented mathematics scholars , seniors or first-year graduate students, who by the time they finish their schooling should have had the opportunity to study in some detail the great discoveries of our subject. What did we know and how and when did we know it? I hope this book is useful toward that goal, especially when it comes to the great achievements of that part of mathematics known as analysis. I have tried to write a complete and thorough account of the elementary theories of functions of a single real variable and functions of a single complex variable. Separating these two subjects does not at all jive with their development historically, and to me it seems unnecessary and potentially confusing to do so. On the other hand, functions of several variables seems to me to be a very different kettle of fish, so I have decided to limit this book by concentrating on one variable at a time. Everyone is taught (told) in school that the area of a circle is given by the formula A = πr2: We are also told that the product of two negatives is a positive, that you cant trisect an angle, and that the square root of 2 is irrational. Students of natural sciences learn that eiπ = 1 and that sin2 + cos2 = 1: More sophisticated students are taught the Fundamental− Theorem of calculus and the Fundamental Theorem of Algebra. -
1 Euclidean Vector Space and Euclidean Affi Ne Space
Profesora: Eugenia Rosado. E.T.S. Arquitectura. Euclidean Geometry1 1 Euclidean vector space and euclidean a¢ ne space 1.1 Scalar product. Euclidean vector space. Let V be a real vector space. De…nition. A scalar product is a map (denoted by a dot ) V V R ! (~u;~v) ~u ~v 7! satisfying the following axioms: 1. commutativity ~u ~v = ~v ~u 2. distributive ~u (~v + ~w) = ~u ~v + ~u ~w 3. ( ~u) ~v = (~u ~v) 4. ~u ~u 0, for every ~u V 2 5. ~u ~u = 0 if and only if ~u = 0 De…nition. Let V be a real vector space and let be a scalar product. The pair (V; ) is said to be an euclidean vector space. Example. The map de…ned as follows V V R ! (~u;~v) ~u ~v = x1x2 + y1y2 + z1z2 7! where ~u = (x1; y1; z1), ~v = (x2; y2; z2) is a scalar product as it satis…es the …ve properties of a scalar product. This scalar product is called standard (or canonical) scalar product. The pair (V; ) where is the standard scalar product is called the standard euclidean space. 1.1.1 Norm associated to a scalar product. Let (V; ) be a real euclidean vector space. De…nition. A norm associated to the scalar product is a map de…ned as follows V kk R ! ~u ~u = p~u ~u: 7! k k Profesora: Eugenia Rosado, E.T.S. Arquitectura. Euclidean Geometry.2 1.1.2 Unitary and orthogonal vectors. Orthonormal basis. Let (V; ) be a real euclidean vector space. De…nition. -
SHEET 14: LINEAR ALGEBRA 14.1 Vector Spaces
SHEET 14: LINEAR ALGEBRA Throughout this sheet, let F be a field. In examples, you need only consider the field F = R. 14.1 Vector spaces Definition 14.1. A vector space over F is a set V with two operations, V × V ! V :(x; y) 7! x + y (vector addition) and F × V ! V :(λ, x) 7! λx (scalar multiplication); that satisfy the following axioms. 1. Addition is commutative: x + y = y + x for all x; y 2 V . 2. Addition is associative: x + (y + z) = (x + y) + z for all x; y; z 2 V . 3. There is an additive identity 0 2 V satisfying x + 0 = x for all x 2 V . 4. For each x 2 V , there is an additive inverse −x 2 V satisfying x + (−x) = 0. 5. Scalar multiplication by 1 fixes vectors: 1x = x for all x 2 V . 6. Scalar multiplication is compatible with F :(λµ)x = λ(µx) for all λ, µ 2 F and x 2 V . 7. Scalar multiplication distributes over vector addition and over scalar addition: λ(x + y) = λx + λy and (λ + µ)x = λx + µx for all λ, µ 2 F and x; y 2 V . In this context, elements of F are called scalars and elements of V are called vectors. Definition 14.2. Let n be a nonnegative integer. The coordinate space F n = F × · · · × F is the set of all n-tuples of elements of F , conventionally regarded as column vectors. Addition and scalar multiplication are defined componentwise; that is, 2 3 2 3 2 3 2 3 x1 y1 x1 + y1 λx1 6x 7 6y 7 6x + y 7 6λx 7 6 27 6 27 6 2 2 7 6 27 if x = 6 . -
Two Fundamental Theorems About the Definite Integral
Two Fundamental Theorems about the Definite Integral These lecture notes develop the theorem Stewart calls The Fundamental Theorem of Calculus in section 5.3. The approach I use is slightly different than that used by Stewart, but is based on the same fundamental ideas. 1 The definite integral Recall that the expression b f(x) dx ∫a is called the definite integral of f(x) over the interval [a,b] and stands for the area underneath the curve y = f(x) over the interval [a,b] (with the understanding that areas above the x-axis are considered positive and the areas beneath the axis are considered negative). In today's lecture I am going to prove an important connection between the definite integral and the derivative and use that connection to compute the definite integral. The result that I am eventually going to prove sits at the end of a chain of earlier definitions and intermediate results. 2 Some important facts about continuous functions The first intermediate result we are going to have to prove along the way depends on some definitions and theorems concerning continuous functions. Here are those definitions and theorems. The definition of continuity A function f(x) is continuous at a point x = a if the following hold 1. f(a) exists 2. lim f(x) exists xœa 3. lim f(x) = f(a) xœa 1 A function f(x) is continuous in an interval [a,b] if it is continuous at every point in that interval. The extreme value theorem Let f(x) be a continuous function in an interval [a,b]. -
Position Management System Online Subject Area
USDA, NATIONAL FINANCE CENTER INSIGHT ENTERPRISE REPORTING Business Intelligence Delivered Insight Quick Reference | Position Management System Online Subject Area What is Position Management System Online (PMSO)? • This Subject Area provides snapshots in time of organization position listings including active (filled and vacant), inactive, and deleted positions. • Position data includes a Master Record, containing basic position data such as grade, pay plan, or occupational series code. • The Master Record is linked to one or more Individual Positions containing organizational structure code, duty station code, and accounting station code data. History • The most recent daily snapshot is available during a given pay period until BEAR runs. • Bi-Weekly snapshots date back to Pay Period 1 of 2014. Data Refresh* Position Management System Online Common Reports Daily • Provides daily results of individual position information, HR Area Report Name Load which changes on a daily basis. Bi-Weekly Organization • Position Daily for current pay and Position Organization with period/ Bi-Weekly • Provides the latest record regardless of previous changes Management PII (PMSO) for historical pay that occur to the data during a given pay period. periods *View the Insight Data Refresh Report to determine the most recent date of refresh Reminder: In all PMSO reports, users should make sure to include: • An Organization filter • PMSO Key elements from the Master Record folder • SSNO element from the Incumbent Employee folder • A time filter from the Snapshot Time folder 1 USDA, NATIONAL FINANCE CENTER INSIGHT ENTERPRISE REPORTING Business Intelligence Delivered Daily Calendar Filters Bi-Weekly Calendar Filters There are three time options when running a bi-weekly There are two ways to pull the most recent daily data in a PMSO report: PMSO report: 1. -
Chapters, in This Chapter We Present Methods Thatare Not Yet Employed by Industrial Robots, Except in an Extremely Simplifiedway
C H A P T E R 11 Force control of manipulators 11.1 INTRODUCTION 11.2 APPLICATION OF INDUSTRIAL ROBOTS TO ASSEMBLY TASKS 11.3 A FRAMEWORK FOR CONTROL IN PARTIALLY CONSTRAINED TASKS 11.4 THE HYBRID POSITION/FORCE CONTROL PROBLEM 11.5 FORCE CONTROL OFA MASS—SPRING SYSTEM 11.6 THE HYBRID POSITION/FORCE CONTROL SCHEME 11.7 CURRENT INDUSTRIAL-ROBOT CONTROL SCHEMES 11.1 INTRODUCTION Positioncontrol is appropriate when a manipulator is followinga trajectory through space, but when any contact is made between the end-effector and the manipulator's environment, mere position control might not suffice. Considera manipulator washing a window with a sponge. The compliance of thesponge might make it possible to regulate the force applied to the window by controlling the position of the end-effector relative to the glass. If the sponge isvery compliant or the position of the glass is known very accurately, this technique could work quite well. If, however, the stiffness of the end-effector, tool, or environment is high, it becomes increasingly difficult to perform operations in which the manipulator presses against a surface. Instead of washing with a sponge, imagine that the manipulator is scraping paint off a glass surface, usinga rigid scraping tool. If there is any uncertainty in the position of the glass surfaceor any error in the position of the manipulator, this task would become impossible. Either the glass would be broken, or the manipulator would wave the scraping toolover the glass with no contact taking place. In both the washing and scraping tasks, it would bemore reasonable not to specify the position of the plane of the glass, but rather to specifya force that is to be maintained normal to the surface. -
Is EE Right for You?
Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science Is EE Right for You? • “Toto, I have a feeling we’re not in Kansas anymore.” • Now that you are here, diii?id you make the right choice? • Electrical engineering is a challenging and satisfying profession. That does not mean it is easy. In fact, with the possible exceptions of medicine or law, it is the MOST difficult. • There are some things you need to consider if you really, really want to be an engineer. • We will consider a few today. EE 1202 Lecture #1 – Why Electrical Engineering? 1 © N. B. Dodge 01/12 Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science Is EE Right for You (2)? • Why did you decide to be an electrical engineer? – Parents will pay for engineering education (it’s what they want). – You like math and science. – A relative is an engineer and you like him/her. – You want to challenge yourself, and engineering seems challenging. – You think you are creative and love technology. – You want to make a difference in society . EE 1202 Lecture #1 – Why Electrical Engineering? 2 © N. B. Dodge 01/12 Erik Jonsson School of Engggineering and The Un ivers ity o f Texas a t Da llas Computer Science The High School “Science Student” Problem • In high school, you were FAR above the average. – And you probably didn’t study too hard, right? • You liked science and math, and they weren’t terribly hard. -
Chapter 5 ANGULAR MOMENTUM and ROTATIONS
Chapter 5 ANGULAR MOMENTUM AND ROTATIONS In classical mechanics the total angular momentum L~ of an isolated system about any …xed point is conserved. The existence of a conserved vector L~ associated with such a system is itself a consequence of the fact that the associated Hamiltonian (or Lagrangian) is invariant under rotations, i.e., if the coordinates and momenta of the entire system are rotated “rigidly” about some point, the energy of the system is unchanged and, more importantly, is the same function of the dynamical variables as it was before the rotation. Such a circumstance would not apply, e.g., to a system lying in an externally imposed gravitational …eld pointing in some speci…c direction. Thus, the invariance of an isolated system under rotations ultimately arises from the fact that, in the absence of external …elds of this sort, space is isotropic; it behaves the same way in all directions. Not surprisingly, therefore, in quantum mechanics the individual Cartesian com- ponents Li of the total angular momentum operator L~ of an isolated system are also constants of the motion. The di¤erent components of L~ are not, however, compatible quantum observables. Indeed, as we will see the operators representing the components of angular momentum along di¤erent directions do not generally commute with one an- other. Thus, the vector operator L~ is not, strictly speaking, an observable, since it does not have a complete basis of eigenstates (which would have to be simultaneous eigenstates of all of its non-commuting components). This lack of commutivity often seems, at …rst encounter, as somewhat of a nuisance but, in fact, it intimately re‡ects the underlying structure of the three dimensional space in which we are immersed, and has its source in the fact that rotations in three dimensions about di¤erent axes do not commute with one another. -
Robotics Engineer
CONTENTS Robotics Engineer at a Glance 6 Introduction 7 Turning Science Fiction into Reality Chapter One 11 What Does a Robotics Engineer Do? Chapter Two 18 How Do You Become a Robotics Engineer? Chapter Three 26 What Skills and Personal Qualities Matter Most —and Why? Chapter Four 31 What Is It Like to Work as a Robotics Engineer? Chapter Five 37 Advancement and Other Job Opportunities Chapter Six 42 What Does the Future Hold for Robotics Engineers? Chapter Seven 49 Interview with a Robotics Engineer Source Notes 53 Find Out More 56 Index 59 Picture Credits 63 About the Author 64 5 ROBOTICS ENGINEER AT A GLANCE te’s Ba cia che so ee de lo As gr gr r’s de ee l D o r o o o t d c h n e t c o a le g s r r m a e a h v t o e l i e g i p u i q H d e Personal Minimum Educational Qualities Requirements Problem solving Creativity Working Conditions Attention to detail Indoors Strong science, math, and computer- programming skills Median Salary $81,591 Percent job increase by 278,000* 2024 Number of jobs *Numbers are for mechanical 5% engineers, a group that includes robotics engineers. Future Job Outlook Source: Bureau of Labor Statistics, Occupational Outlook Handbook. www.bls.gov. 6 CHAPTER 3 What Skills and Personal Qualities Matter Most—and Why? First and foremost, robotics engineers must be very good prob- lem solvers. They must have suffi cient technical skill to recognize and understand a problem and enough creativity to think up an original solution. -
Photonic Design Engineer
Photonic Design Engineer Are you looking for the ultimate startup challenge? Have you always wanted to transform innovative technology into real products? Are you ready to join OPTIUS among the first employees with all the advantages and opportunities? Optius is a new startup with the vision to transform the field of efficient AI computations by using optical computing. By joining OPTIUS, you are contributing to a growing team of motivated entrepreneurs and researchers passionate about bringing this vision into reality. The Photonic Design Engineer role will involve the design, optimization, and layout of photonic integrated circuits (PICs) and photonic devices. Your opportunity and benefits: • Solve problems by commercializing cutting edge technology – Major impact! • Mentorship, coaching and support – we are here for you! • Cool Startup environment – celebrations, endless lattes, healthy snacks What we offer: • Competitive compensation package • Opportunity for growth and personal development • Insurance benefits such as health, dental and vision • Cool Startup environment – celebrations, endless coffee, healthy snacks • Lunch and Learns What your day-today will look like: • Design and optimize photonic integrated circuits (PIC’s) • Layout photonic devices with common EDA • Conduct numerical electromagnetic simulation of photonic devices • Interacting with photonic foundries to understand design environment and rules • Designing optical bench experiments for device characterization • Collaborating with the team on research and development -
Scalar-Tensor Theories of Gravity: Some Personal History
history-st-cuba-slides 8:31 May 27, 2008 1 SCALAR-TENSOR THEORIES OF GRAVITY: SOME PERSONAL HISTORY Cuba meeting in Mexico 2008 Remembering Johnny Wheeler (JAW), 1911-2008 and Bob Dicke, 1916-1997 We all recall Johnny as one of the most prominent and productive leaders of relativ- ity research in the United States starting from the late 1950’s. I recall him as the man in relativity when I entered Princeton as a graduate student in 1957. One of his most recent students on the staff there at that time was Charlie Misner, who taught a really new, interesting, and, to me, exciting type of relativity class based on then “modern mathematical techniques involving topology, bundle theory, differential forms, etc. Cer- tainly Misner had been influenced by Wheeler to pursue these then cutting-edge topics and begin the re-write of relativity texts that ultimately led to the massive Gravitation or simply “Misner, Thorne, and Wheeler. As I recall (from long! ago) Wheeler was the type to encourage and mentor young people to investigate new ideas, especially mathe- matical, to develop and probe new insights into the physical universe. Wheeler himself remained, I believe, more of a “generalist, relying on experts to provide details and rigorous arguments. Certainly some of the world’s leading mathematical work was being done only a brief hallway walk away from Palmer Physical Laboratory to Fine Hall. Perhaps many are unaware that Bob Dicke had been an undergraduate student of Wheeler’s a few years earlier. It was Wheeler himself who apparently got Bob thinking about the foundations of Einstein’s gravitational theory, in particular, the ever present mysteries of inertia.