The presented theoretical results, practical solutions and guidelines will be useful for both researchers working in the area of engineering sciences and for practitioners solving industrial problems.
with mixed boundary conditions.
The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method.
The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed.
• Includes analytical solving of mixed boundary value problems
• Introduces modern asymptotic and summation procedures
• Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates
• Covers statics, dynamics and stability of plates with mixed boundary conditions
• Explains links between the Adomian and homotopy perturbation approaches
Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.
The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous sytems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
This book provides a theoretical background on the analysis of various kinds of mechatronics systems, along with their computational analysis, control, optimization as well as laboratory investigations.
The presented theoretical results, practical solutions and guidelines will be useful for both researchers working in the area of engineering sciences and for practitioners solving industrial problems.
The studies give deep insight into new perspectives in analysis, simulation, and optimization of dynamical systems, emphasizing directions for future research. Broadly outlined topics covered include: bifurcation and chaos in dynamical systems, asymptotic methods in nonlinear dynamics, dynamics in life sciences and bioengineering, original numerical methods of vibration analysis, control in dynamical systems, stability of dynamical systems, vibrations of lumped and continuous systems, non-smooth systems, engineering systems and differential equations, mathematical approaches to dynamical systems, and mechatronics.
Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples and engineering intuition.
The scientific background used is well balanced between elementary and advanced level, making it as a unique self-contained source for both theoretically and application oriented graduate and doctoral students, university teachers, researchers and engineers of mechanical, civil and mechatronic engineering.
Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler–Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic–plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.
The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.Contents:Bifurcational and Chaotic Dynamics of Simple Structural Members:BeamsPlatesPanelsShellsIntroduction to Fractal Dynamics:Cantor Set and Cantor DustKoch Snowflake1D MapsSharkovsky's TheoremJulia SetMandelbrot's SetIntroduction to Chaos and Wavelets:Routes to ChaosQuantifying Chaotic DynamicsSimple Chaotic Models:IntroductionAutonomous SystemsNon-Autonomous SystemsDiscrete and Continuous Dissipative Systems:IntroductionLinear FrictionNonlinear FrictionHysteretic FrictionImpact DampingDamping in Continuous 1D SystemsEuler-Bernoulli Beams:IntroductionPlanar BeamsLinear Planar Beams and Stationary Temperature FieldsCurvilinear Planar Beams and Stationary Temperature and Electrical FieldsBeams with Elasto-Plastic DeformationsMulti-Layer BeamsTimoshenko and Sheremetev-Pelekh Beams:The Timoshenko BeamsThe Sheremetev-Pelekh BeamsConcluding RemarksPanels:Infinite Length PanelsCylindrical Panels of Infinite LengthPlates and Shells:Plates with Initial ImperfectionsFlexible Axially-Symmetric Shells
Readership: Post-graduate and doctoral students, applied mathematicians, physicists, mechanical and civil engineers.
Key Features:Includes fascinating and rich dynamics exhibited by simple structural members and by the solution properties of the governing 1D non-linear PDEs, suitable for applied mathematicians and physicistsCovers a wide variety of the studied PDEs, their validated reduction to ODEs, classical and non-classical methods of analysis, influence of various boundary conditions and control parameters, as well as the illustrative presentation of the obtained results in the form of colour 2D and 3D figures and vibration type charts and scalesContains originally discovered, illustrated and discussed novel and/or modified classical scenarios of transition from regular to chaotic dynamics exhibited by 1D structural members, showing a way to control chaotic and bifurcational dynamics, with directions to study other dynamical systems modeled by chains of nonlinear oscillators
“Artfully envisions a breathtakingly better world.” —Los Angeles Times
“Elaborate, smart and persuasive.” —The Boston Globe
“A pleasure to read.” —The Wall Street Journal
One of CBS News’s Best Fall Books of 2005 • Among St Louis Post-Dispatch’s Best Nonfiction Books of 2005 • One of Amazon.com’s Best Science Books of 2005
A radical and optimistic view of the future course of human development from the bestselling author of How to Create a Mind and The Age of Spiritual Machines who Bill Gates calls “the best person I know at predicting the future of artificial intelligence”
For over three decades, Ray Kurzweil has been one of the most respected and provocative advocates of the role of technology in our future. In his classic The Age of Spiritual Machines, he argued that computers would soon rival the full range of human intelligence at its best. Now he examines the next step in this inexorable evolutionary process: the union of human and machine, in which the knowledge and skills embedded in our brains will be combined with the vastly greater capacity, speed, and knowledge-sharing ability of our creations.
From the Trade Paperback edition.
Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.
Artificial Intelligence helps choose what books you buy, what movies you see, and even who you date. It puts the "smart" in your smartphone and soon it will drive your car. It makes most of the trades on Wall Street, and controls vital energy, water, and transportation infrastructure. But Artificial Intelligence can also threaten our existence.
In as little as a decade, AI could match and then surpass human intelligence. Corporations and government agencies are pouring billions into achieving AI's Holy Grail—human-level intelligence. Once AI has attained it, scientists argue, it will have survival drives much like our own. We may be forced to compete with a rival more cunning, more powerful, and more alien than we can imagine.
Through profiles of tech visionaries, industry watchdogs, and groundbreaking AI systems, Our Final Invention explores the perils of the heedless pursuit of advanced AI. Until now, human intelligence has had no rival. Can we coexist with beings whose intelligence dwarfs our own? And will they allow us to?
If you ever regretted not taking physics in college--or simply want to know how to think like a physicist--this is the book for you. In this bestselling introduction, physicist Leonard Susskind and hacker-scientist George Hrabovsky offer a first course in physics and associated math for the ardent amateur. Challenging, lucid, and concise, The Theoretical Minimum provides a tool kit for amateur scientists to learn physics at their own pace.
Ray Kurzweil is arguably today’s most influential—and often controversial—futurist. In How to Create a Mind, Kurzweil presents a provocative exploration of the most important project in human-machine civilization—reverse engineering the brain to understand precisely how it works and using that knowledge to create even more intelligent machines.
Kurzweil discusses how the brain functions, how the mind emerges from the brain, and the implications of vastly increasing the powers of our intelligence in addressing the world’s problems. He thoughtfully examines emotional and moral intelligence and the origins of consciousness and envisions the radical possibilities of our merging with the intelligent technology we are creating.
Certain to be one of the most widely discussed and debated science books of the year, How to Create a Mind is sure to take its place alongside Kurzweil’s previous classics which include Fantastic Voyage: Live Long Enough to Live Forever and The Age of Spiritual Machines.
From the Hardcover edition.
Jeff Hawkins, the man who created the PalmPilot, Treo smart phone, and other handheld devices, has reshaped our relationship to computers. Now he stands ready to revolutionize both neuroscience and computing in one stroke, with a new understanding of intelligence itself.
Hawkins develops a powerful theory of how the human brain works, explaining why computers are not intelligent and how, based on this new theory, we can finally build intelligent machines.
The brain is not a computer, but a memory system that stores experiences in a way that reflects the true structure of the world, remembering sequences of events and their nested relationships and making predictions based on those memories. It is this memory-prediction system that forms the basis of intelligence, perception, creativity, and even consciousness.
In an engaging style that will captivate audiences from the merely curious to the professional scientist, Hawkins shows how a clear understanding of how the brain works will make it possible for us to build intelligent machines, in silicon, that will exceed our human ability in surprising ways.
Written with acclaimed science writer Sandra Blakeslee, On Intelligence promises to completely transfigure the possibilities of the technology age. It is a landmark book in its scope and clarity.
Now updated with 30% new material, Roark Formulas for Stress and Strain, Seventh Edition, is the ultimate resource for designers, engineers, and analysts who need to calculate loads and stress. This landmark reference from Warren Young and Richard Budynas provides you with equations and diagrams of structural properties in an easy-to-use, thumb-through format. Updated, with a user-friendly page layout, this new edition includes expanded coverage of joints, bearing and shear stress, experimental stress analysis, and stress concentrations, as well as material behavior coverage and stress and strain measurement. You’ll also find expanded tables and cases; improved notations and figures in the tables; consistent table and equation numbering; and verification of correction factors.
The Mechanical Engineering Reference Manual is the most comprehensive textbook for the Mechanical PE exam. This book's time-tested organization and clear explanations start with the basics to help you quickly get up to speed on common mechanical engineering concepts. Together, the 76 chapters provide an in-depth review of NCEES Mechanical PE exam topics. The extensive index contains thousands of terms, most indexed in a variety of ways, in anticipation of how you'll search for them.
Features of the Mechanical Engineering Reference Manual: • over 120 appendices containing essential support material • over 375 clarifying example problems • thousands of equations, figures, and tables • industry-standard terminology and nomenclature • equal support of U.S. customary and SI units
After you pass your exam, the Mechanical Engineering Reference Manual will continue to serve as an invaluable reference throughout your mechanical engineering career.
Topics Covered: • Dynamics and Vibrations: Kinematics; Kinetics; Power Transmission Systems; Vibrating Systems • Materials: Engineering Materials Properties and Testing; Thermal Treatment of Metals • Fluids: Fluid Properties; Fluid Statics; Fluid Flow Parameters; Fluid Dynamics; Hydraulic Machines • Power Cycles: Vapor, Combustion, and Nuclear Power Cycles; Refrigeration and Gas Compression Cycles • HVAC: Psychrometrics; Fans, Ductwork, and Ventilation; Heating and Cooling Loads; Air Conditioning Systems • Heat Transfer: Natural Convection; Evaporation; Condensation; Forced Convection; Radiation • Machine Design: Basic and Advanced Machine Design; Pressure Vessels • Thermodynamics: Inorganic Chemistry; Fuels and Combustion; Properties of Substances • Control Systems: Modeling and Analysis of Engineering Systems • Plant Engineering: Manufacturing Processes; Instrumentation and Measurements; Materials Handling and Processing; Fire Protection Systems; Environmental Pollutants and Remediation; Hazardous Material Storage and Disposal • Fundamentals: Math Review; Probability; Statics; Engineering Economic Analysis • Law and Ethics: Engineering Law; Ethics
What's New in This Edition: • 36 chapters with new material, and 46 chapters with revisions to existing material • 300 new equations, and 128 updated equations • 27 new tables, and 31 updated tables • 7 new examples, and 34 updated examples • 10 new appendices, and 27 updated appendices • 35 new figures, and 28 updated figures • 1,094 new index entries, and 108 updated index entries
Illustrating turbomachinery, vibration severity levels, condition monitoring, and rotor vibration cause identification, Rotating Machinery Vibration
Provides a primer on vibration fundamentals
Highlights calculation of rotor unbalance response and rotor self-excited vibration
Demonstrates calculation of rotor balancing weights
Furnishes PC codes for lateral rotor vibration analyses
Treats bearing, seal, impeller, and blade effects on rotor vibration
Describes modes, excitation, and stability of computer models
Includes extensive PC data coefficient files on bearing dynamics
Providing comprehensive descriptions of vibration symptoms for rotor unbalance, dynamic instability, rotor-stator rubs, misalignment, loose parts, cracked shafts, and rub-induced thermal bows, Rotating Machinery Vibration is an essential reference for mechanical, chemical, design, manufacturing, materials, aerospace, and reliability engineers; and specialists in vibration, rotating machinery, and turbomachinery; and an ideal text for upper-level undergraduate and graduate students in these disciplines.
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a new skill set, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating material. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life.
In A Mind for Numbers, Dr. Oakley lets us in on the secrets to learning effectively—secrets that even dedicated and successful students wish they’d known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there’s only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. The learning strategies in this book apply not only to math and science, but to any subject in which we struggle. We all have what it takes to excel in areas that don't seem to come naturally to us at first, and learning them does not have to be as painful as we might think!
From the Trade Paperback edition.
Combining leading research from both academia and industry onto a single platform, Energy Harvesting Technologies serves as an important reference for researchers and engineers involved with power sources, sensor networks and smart materials.
Drawing on physics and mechanical engineering, Steven Vogel looks at how animals swim and fly, modes of terrestrial locomotion, organism responses to winds and water currents, circulatory and suspension-feeding systems, and the relationship between size and mechanical design. He also investigates links between the properties of biological materials--such as spider silk, jellyfish jelly, and muscle--and their structural and functional roles. Early chapters and appendices introduce relevant physical variables for quantification, and problem sets are provided at the end of each chapter. Comparative Biomechanics is useful for physical scientists and engineers seeking a guide to state-of-the-art biomechanics. For a wider audience, the textbook establishes the basic biological context for applied areas--including ergonomics, orthopedics, mechanical prosthetics, kinesiology, sports medicine, and biomimetics--and provides materials for exhibit designers at science museums.Problem sets at the ends of chapters Appendices cover basic background information Updated and expanded documentation and materials Revised figures and text Increased coverage of friction, viscoelastic materials, surface tension, diverse modes of locomotion, and biomimetics
* Beautifully illustrated with images relating to Newton’s life and works
* New introductions, specially written for this collection, by Professor Kenneth Richard Seddon, OBE (QUILL, The Queen’s University of Belfast)
* Images of how the books were first published, giving your eReader a taste of the original texts
* Excellent formatting of the texts
* Key works are fully illustrated with their original diagrams
* Features three biographies - discover Newton’s intriguing life
* Scholarly ordering of texts into chronological order and genres
Please visit www.delphiclassics.com to browse through our range of exciting titles
PHILOSOPHIÆ NATURALIS PRINCIPIA MATHEMATICA
THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY (MOTTE TRANSLATION)
THE CHRONOLOGY OF ANCIENT KINGDOMS AMENDED
OBSERVATIONS ON DANIEL AND THE APOCALYPSE OF ST. JOHN
AN HISTORICAL ACCOUNT OF TWO NOTABLE CORRUPTIONS OF SCRIPTURE
MEMOIRS OF SIR ISAAC NEWTON’S LIFE by William Stukeley
SIR ISAAC NEWTON by Sarah K. Bolton
SIR ISAAC NEWTON by Henry Martyn Taylor
Please visit www.delphiclassics.com to browse through our range of exciting titles or to purchase this eBook as a Parts Edition of individual eBooks
Helps Students Better Understand Numerical Methods through Use of MATLAB®
The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions.
All the Material Needed for a Numerical Analysis Course
Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.
All mechanical equipment in motion generates a vibration profile, or signature, that reflects its operating condition. This is true regardless of speed or whether the mode of operation is rotation, reciprocation, or linear motion. There are several predictive maintenance techniques used to monitor and analyze critical machines, equipment, and systems in a typical plant. These include vibration analysis, ultrasonics, thermography, tribology, process monitoring, visual inspection, and other nondestructive analysis techniques. Of these techniques, vibration analysis is the dominant predictive maintenance technique used with maintenance management programs, and this book explains the basic theory, applications, and benefits in one easy-to-absorb volume that plant staff will find invaluable.
This is the second book in a new series published by Butterworth-Heinemann in association with PLANT ENGINEERING magazine. PLANT ENGINEERING fills a unique information need for the men and women who operate and maintain industrial plants. It bridges the information gap between engineering education and practical application. As technology advances at increasingly faster rates, this information service is becoming more and more important. Since its first issue in 1947, PLANT ENGINEERING has stood as the leading problem-solving information source for America's industrial plant engineers, and this book series will effectively contribute to that resource and reputation.Provides information essential to industrial troubleshooting investigationsDescribes root-cause failure analysisIncorporates detailed equipment-design guidelines
Helping you overcome these hurdles, Hydraulic Power System Analysis demonstrates modern computer-aided analytical techniques used to model nonlinear, dynamic fluid power systems. Following an overview of fluid power, the authors examine various relevant fluid properties, energy calculations, and steady state and dynamic analysis along with a review of automatic control theory. Turning to modeling, the next few chapters address valves and motors and then apply dynamic modeling to examples relating to pumps, hydrostatic transmissions, and valves. The book includes a unique chapter showing how to combine flow resistance equations with the differential equations governing dynamic system performance. The final chapter translates electrical circuit theory concepts to noise attenuation in fluid power systems.
Illustrated with many equations, practical computer modeling examples, and exercises, Hydraulic Power System Analysis provides a much-needed modernization of dynamic modeling for fluid power systems using powerful computational tools.
About the authors . . .
D. M. PIRRO is the Equipment Builder and OEM Manager, ExxonMobil Corporation, Fairfax, Virginia. The author or contributing editor of several scholarly articles on synthetic lubes, environmental awareness applications, grease technology, lubricant interchangeability, and oil analysis, Mr. Pirro is a Certified Lubrication Specialist and a member of the Society of Tribologists and Lubrication Engineers and the Association of Manufacturing Technology. He received the B.S. degree (1978) in mechanical engineering and the B.A. degree (1978) in business administration from Rutgers University, New Brunswick, New Jersey.
A. A. WESSOL is a part-time Lubrication Consultant for the ExxonMobil Corporation in Manassas, Virginia. Mr. Wessol retired from the Mobil Corporation after 24 years in various advanced technical positions. The author or coauthor of numerous professional papers on the environmental aspects of lubrication, plant engineering, hydraulics, and pneumatics, he received the B.S. degree (1972) in mathematics, physics, and chemistry from the University of Pittsburgh, Pennsylvania.
Finite Element Modeling and Simulation with ANSYS Workbench combines finite element theory with real-world practice. Providing an introduction to finite element modeling and analysis for those with no prior experience, and written by authors with a combined experience of 30 years teaching the subject, this text presents FEM formulations integrated with relevant hands-on applications using ANSYS Workbench for finite element analysis (FEA). Incorporating the basic theories of FEA and the use of ANSYS Workbench in the modeling and simulation of engineering problems, the book also establishes the FEM method as a powerful numerical tool in engineering design and analysis.
Include FEA in Your Design and Analysis of Structures Using ANSYS Workbench
The authors reveal the basic concepts in FEA using simple mechanics problems as examples, and provide a clear understanding of FEA principles, element behaviors, and solution procedures. They emphasize correct usage of FEA software, and techniques in FEA modeling and simulation. The material in the book discusses one-dimensional bar and beam elements, two-dimensional plane stress and plane strain elements, plate and shell elements, and three-dimensional solid elements in the analyses of structural stresses, vibrations and dynamics, thermal responses, fluid flows, optimizations, and failures. Contained in 12 chapters, the text introduces ANSYS Workbench through detailed examples and hands-on case studies, and includes homework problems and projects using ANSYS Workbench software that are provided at the end of each chapter.Covers solid mechanics and thermal/fluid FEA Contains ANSYS Workbench geometry input files for examples and case studies Includes two chapters devoted to modeling and solution techniques, design optimization, fatigue, and buckling failure analysis Provides modeling tips in case studies to provide readers an immediate opportunity to apply the skills they learn in a problem-solving context
Finite Element Modeling and Simulation with ANSYS Workbench benefits upper-level undergraduate students in all engineering disciplines, as well as researchers and practicing engineers who use the finite element method to analyze structures.
The coverage of the book includes 13 topics relevant to classical mechanics, such as integration of one-dimensional equations of motion; the Hamiltonian equations of motion; and adiabatic invariants.
The book will be of great use to physics students studying classical mechanics.
The math we learn in school can seem like a dull set of rules, laid down by the ancients and not to be questioned. In How Not to Be Wrong, Jordan Ellenberg shows us how terribly limiting this view is: Math isn’t confined to abstract incidents that never occur in real life, but rather touches everything we do—the whole world is shot through with it.
Math allows us to see the hidden structures underneath the messy and chaotic surface of our world. It’s a science of not being wrong, hammered out by centuries of hard work and argument. Armed with the tools of mathematics, we can see through to the true meaning of information we take for granted: How early should you get to the airport? What does “public opinion” really represent? Why do tall parents have shorter children? Who really won Florida in 2000? And how likely are you, really, to develop cancer?
How Not to Be Wrong presents the surprising revelations behind all of these questions and many more, using the mathematician’s method of analyzing life and exposing the hard-won insights of the academic community to the layman—minus the jargon. Ellenberg chases mathematical threads through a vast range of time and space, from the everyday to the cosmic, encountering, among other things, baseball, Reaganomics, daring lottery schemes, Voltaire, the replicability crisis in psychology, Italian Renaissance painting, artificial languages, the development of non-Euclidean geometry, the coming obesity apocalypse, Antonin Scalia’s views on crime and punishment, the psychology of slime molds, what Facebook can and can’t figure out about you, and the existence of God.
Ellenberg pulls from history as well as from the latest theoretical developments to provide those not trained in math with the knowledge they need. Math, as Ellenberg says, is “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.” With the tools of mathematics in hand, you can understand the world in a deeper, more meaningful way. How Not to Be Wrong will show you how.
Taking the bang-whiz-thud approach, Denny first talks about internal ballistics—Bang!—from before gunpowder to the development of modern firearms. External ballistics—Whiz!—are next, with discussions about short- and long-range trajectories. Denny’s lesson ends with a Thud!—an explanation of terminal ballistics.
Throughout, Denny conveys applicable physics principles in a way that will appeal to technology buffs and ballistics enthusiasts alike. His fun and factual explanations are free of complicated equations; notes cover the key aspects of ballistics physics for the more technically inclined.
Denny has perfected this engaging balance of science and story. For study or hobby, Their Arrows Will Darken the Sun is an entertaining guide to the world of ballistics.