Classical mechanics : a computational approach with examples using mathematica and Python /
Kulp, Christopher W.,
Classical mechanics : a computational approach with examples using mathematica and Python / Christopher W. Kulp, Vasilis Pagonis. - 1st. - 1 online resource (440 pages) : 192 illustrations
Chapter 1. Foundations of Motion and Computation Chapter 2. Single-Particle Motion in One Dimesnison Chapter 3.Motion in Two and Three Dimensions Chapter 4. Momentum, Angular Momentum, and Multi-Particle Chapter 5. Energy Chapter 6. Harmonic Oscillations Chapter 7. The Calculus of Variations Chapter 8. Lagrangian and Hamiltonian Dynamics Chapter 9. Central Forces and Planetry Motions Chapter 10. Motion in Non-Inertial Reference Frames Chapter 11. Rigid Body Motion Chapter 12. Coupled Oscillations Chapter 13. Nonlinear Systems.
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Chapter 1: The Foundations of Motion and Computation -- 1.1 THE WORLD OF PHYSICS -- 1.2 THE BASICS OF CLASSICAL MECHANICS -- 1.2.1 The Basic Descriptors of Motion -- 1.2.1.1 Position and Displacement -- 1.2.1.2 Velocity -- 1.2.1.3 Acceleration -- 1.2.2 Mass and Force -- 1.2.2.1 Mass -- 1.2.2.2 Force -- 1.3 NEWTON'S LAWS OF MOTION -- 1.3.1 Newton's First Law -- 1.3.2 Newton's second law -- 1.3.3 Newton's third law -- 1.4 REFERENCE FRAMES -- 1.5 COMPUTATION IN PHYSICS 1.5.1 The Use of Computation in Physics -- 1.5.2 Different Computational Tools -- 1.5.3 Some Warnings -- 1.6 CLASSICAL MECHANICS IN THE MODERN WORLD -- 1.7 CHAPTER SUMMARY -- 1.8 END-OF-CHAPTER PROBLEMS -- Chapter 2: Single-Particle Motion in One Dimension -- 2.1 EQUATIONS OF MOTION -- 2.2 ORDINARY DIFFERENTIAL EQUATIONS -- 2.3 CONSTANT FORCES -- 2.4 TIME-DEPENDENT FORCES -- 2.5 AIR RESISTANCE AND VELOCITY-DEPENDENT FORCES -- 2.6 POSITION-DEPENDENT FORCES -- 2.7 NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS -- 2.8 CHAPTER SUMMARY -- 2.9 END-OF-CHAPTER PROBLEMS Chapter 3: Motion in Two and Three Dimensions -- 3.1 POSITION, VELOCITY, AND ACCELERATION IN CARTESIAN COORDI-NATE SYSTEMS -- 3.2 VECTOR PRODUCTS -- 3.2.1 The Dot Product -- 3.2.2 The Cross Product -- 3.3 POSITION, VELOCITY, AND ACCELERATION IN NON-CARTESIAN COORDINATE SYSTEMS -- 3.3.1 Polar Coordinates -- 3.3.2 Position, Velocity, and Acceleration in Cylindrical Coordinates -- 3.3.3 Position, Velocity, and Acceleration in Spherical Coordinates -- 3.4 THE GRADIENT, DIVERGENCE, AND CURL -- 3.4.1 The Gradient -- 3.4.2 The Divergence -- 3.4.3 The Curl 3.4.4 Second Derivatives with the Del Operator -- 3.5 CHAPTER SUMMARY -- 3.6 END-OF-CHAPTER PROBLEMS -- Chapter 4: Momentum, Angular Momentum, and Multiparticle Systems -- 4.1 CONSERVATION OF MOMENTUM AND NEWTON'S THIRD LAW -- 4.2 ROCKETS -- 4.3 CENTER OF MASS -- 4.4 NUMERICAL INTEGRATION AND THE CENTER OF MASS -- 4.4.1 Trapezoidal Rule -- 4.4.2 Simpson's Rule -- 4.5 MOMENTUM OF A SYSTEM OF MULTIPLE PARTICLES -- 4.6 ANGULAR MOMENTUM OF A SINGLE PARTICLE -- 4.7 ANGULAR MOMENTUM OF MULTIPLE PARTICLES -- 4.8 CHAPTER SUMMARY -- 4.9 END-OF-CHAPTER PROBLEMS -- Chapter 5: Energy 5.1 WORK AND ENERGY IN ONE-DIMENSIONAL SYSTEMS -- 5.2 POTENTIAL ENERGY AND EQUILIBRIUM POINTS IN ONE-DIMENSIONAL SYSTEMS -- 5.3 WORK AND LINE INTEGRALS -- 5.4 THE WORK-KINETIC ENERGY THEOREM, REVISITED -- 5.5 CONSERVATIVE FORCES AND POTENTIAL ENERGY -- 5.6 ENERGY AND MULTIPARTICLE SYSTEMS -- 5.7 CHAPTER SUMMARY -- 5.8 END-OF-CHAPTER PROBLEMS -- Chapter 6: Harmonic Oscillations -- 6.1 DIFFERENTIAL EQUATIONS -- 6.2 THE SIMPLE HARMONIC OSCILLATOR -- 6.2.1 The Equation of Motion of the Simple Harmonic Oscillator -- 6.2.2 Potential and Kinetic Energy in Simple Harmonic Motion
Classical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation. Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics. It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics. Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms A solutions manual is available via the Routledge Instructor Hub and extra code is available via the Support Material tab
9781351024365 1351024361 9781351024389 1351024388 9781351024372 135102437X 9781351024358 1351024353
10.1201/9781351024389. doi
Mathematica (Computer file)
Python (Computer program language)
Mechanics.
Mechanics--Data processing.
SCIENCE / Mathematical Physics
MATHEMATICS / Arithmetic
QA805
531
Classical mechanics : a computational approach with examples using mathematica and Python / Christopher W. Kulp, Vasilis Pagonis. - 1st. - 1 online resource (440 pages) : 192 illustrations
Chapter 1. Foundations of Motion and Computation Chapter 2. Single-Particle Motion in One Dimesnison Chapter 3.Motion in Two and Three Dimensions Chapter 4. Momentum, Angular Momentum, and Multi-Particle Chapter 5. Energy Chapter 6. Harmonic Oscillations Chapter 7. The Calculus of Variations Chapter 8. Lagrangian and Hamiltonian Dynamics Chapter 9. Central Forces and Planetry Motions Chapter 10. Motion in Non-Inertial Reference Frames Chapter 11. Rigid Body Motion Chapter 12. Coupled Oscillations Chapter 13. Nonlinear Systems.
Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Chapter 1: The Foundations of Motion and Computation -- 1.1 THE WORLD OF PHYSICS -- 1.2 THE BASICS OF CLASSICAL MECHANICS -- 1.2.1 The Basic Descriptors of Motion -- 1.2.1.1 Position and Displacement -- 1.2.1.2 Velocity -- 1.2.1.3 Acceleration -- 1.2.2 Mass and Force -- 1.2.2.1 Mass -- 1.2.2.2 Force -- 1.3 NEWTON'S LAWS OF MOTION -- 1.3.1 Newton's First Law -- 1.3.2 Newton's second law -- 1.3.3 Newton's third law -- 1.4 REFERENCE FRAMES -- 1.5 COMPUTATION IN PHYSICS 1.5.1 The Use of Computation in Physics -- 1.5.2 Different Computational Tools -- 1.5.3 Some Warnings -- 1.6 CLASSICAL MECHANICS IN THE MODERN WORLD -- 1.7 CHAPTER SUMMARY -- 1.8 END-OF-CHAPTER PROBLEMS -- Chapter 2: Single-Particle Motion in One Dimension -- 2.1 EQUATIONS OF MOTION -- 2.2 ORDINARY DIFFERENTIAL EQUATIONS -- 2.3 CONSTANT FORCES -- 2.4 TIME-DEPENDENT FORCES -- 2.5 AIR RESISTANCE AND VELOCITY-DEPENDENT FORCES -- 2.6 POSITION-DEPENDENT FORCES -- 2.7 NUMERICAL SOLUTIONS OF DIFFERENTIAL EQUATIONS -- 2.8 CHAPTER SUMMARY -- 2.9 END-OF-CHAPTER PROBLEMS Chapter 3: Motion in Two and Three Dimensions -- 3.1 POSITION, VELOCITY, AND ACCELERATION IN CARTESIAN COORDI-NATE SYSTEMS -- 3.2 VECTOR PRODUCTS -- 3.2.1 The Dot Product -- 3.2.2 The Cross Product -- 3.3 POSITION, VELOCITY, AND ACCELERATION IN NON-CARTESIAN COORDINATE SYSTEMS -- 3.3.1 Polar Coordinates -- 3.3.2 Position, Velocity, and Acceleration in Cylindrical Coordinates -- 3.3.3 Position, Velocity, and Acceleration in Spherical Coordinates -- 3.4 THE GRADIENT, DIVERGENCE, AND CURL -- 3.4.1 The Gradient -- 3.4.2 The Divergence -- 3.4.3 The Curl 3.4.4 Second Derivatives with the Del Operator -- 3.5 CHAPTER SUMMARY -- 3.6 END-OF-CHAPTER PROBLEMS -- Chapter 4: Momentum, Angular Momentum, and Multiparticle Systems -- 4.1 CONSERVATION OF MOMENTUM AND NEWTON'S THIRD LAW -- 4.2 ROCKETS -- 4.3 CENTER OF MASS -- 4.4 NUMERICAL INTEGRATION AND THE CENTER OF MASS -- 4.4.1 Trapezoidal Rule -- 4.4.2 Simpson's Rule -- 4.5 MOMENTUM OF A SYSTEM OF MULTIPLE PARTICLES -- 4.6 ANGULAR MOMENTUM OF A SINGLE PARTICLE -- 4.7 ANGULAR MOMENTUM OF MULTIPLE PARTICLES -- 4.8 CHAPTER SUMMARY -- 4.9 END-OF-CHAPTER PROBLEMS -- Chapter 5: Energy 5.1 WORK AND ENERGY IN ONE-DIMENSIONAL SYSTEMS -- 5.2 POTENTIAL ENERGY AND EQUILIBRIUM POINTS IN ONE-DIMENSIONAL SYSTEMS -- 5.3 WORK AND LINE INTEGRALS -- 5.4 THE WORK-KINETIC ENERGY THEOREM, REVISITED -- 5.5 CONSERVATIVE FORCES AND POTENTIAL ENERGY -- 5.6 ENERGY AND MULTIPARTICLE SYSTEMS -- 5.7 CHAPTER SUMMARY -- 5.8 END-OF-CHAPTER PROBLEMS -- Chapter 6: Harmonic Oscillations -- 6.1 DIFFERENTIAL EQUATIONS -- 6.2 THE SIMPLE HARMONIC OSCILLATOR -- 6.2.1 The Equation of Motion of the Simple Harmonic Oscillator -- 6.2.2 Potential and Kinetic Energy in Simple Harmonic Motion
Classical Mechanics: A Computational Approach with Examples using Python and Mathematica provides a unique, contemporary introduction to classical mechanics, with a focus on computational methods. In addition to providing clear and thorough coverage of key topics, this textbook includes integrated instructions and treatments of computation. Full of pedagogy, it contains both analytical and computational example problems within the body of each chapter. The example problems teach readers both analytical methods and how to use computer algebra systems and computer programming to solve problems in classical mechanics. End-of-chapter problems allow students to hone their skills in problem solving with and without the use of a computer. The methods presented in this book can then be used by students when solving problems in other fields both within and outside of physics. It is an ideal textbook for undergraduate students in physics, mathematics, and engineering studying classical mechanics. Features: Gives readers the "big picture" of classical mechanics and the importance of computation in the solution of problems in physics Numerous example problems using both analytical and computational methods, as well as explanations as to how and why specific techniques were used Online resources containing specific example codes to help students learn computational methods and write their own algorithms A solutions manual is available via the Routledge Instructor Hub and extra code is available via the Support Material tab
9781351024365 1351024361 9781351024389 1351024388 9781351024372 135102437X 9781351024358 1351024353
10.1201/9781351024389. doi
Mathematica (Computer file)
Python (Computer program language)
Mechanics.
Mechanics--Data processing.
SCIENCE / Mathematical Physics
MATHEMATICS / Arithmetic
QA805
531