Computer Algebra Recipes for Classical Mechanics, Volume 2

Richard H. Enns, George C. McGuire

Springer Science & Business Media, Nov 22, 2002 - Mathematics - 265 pages

Hundreds of novel and innovative computer algebra "recipes" will enable readers starting at the second year undergraduate level to easily and rapidly solve and explore most problems they encounter in their classical mechanics studies. While the aim is not to try and teach the fundamentals of the subject, the recipes are organized to correlate with topics found in standard classical mechanics texts.

Using the powerful computer algebra system MAPLE (Release 8) --- no prior knowledge of MAPLE is presumed --- the relevant command structures are explained on a need-to-know basis as the recipes are developed. This is a self-contained and standalone text, similar only in style and format to Computer Algebra Recipes: A Gourmet's Guide to the Mathematical Models of Science, ISBN 0-387-95148-2, Springer New York. The computer algebra recipes are introduced in the context of interesting tales, a teaching approach that has been successfully classroom tested by the authors.

This new problem-solving guide can serve in a variety of ways: for use in the classroom or self-study, for reference, or as a text for an on-line course. Science professionals, engineers who need to quickly solve complex classical mechanics problems relevant to their work, and instructors seeking a modern approach to teaching this venerable subject will find this work an invaluable resource.

Contents

• INTRODUCTION: 1
• B The Spiral Approach to Learning Mechanics: 2
• C Maple Help: 3
• D Introductory Recipe: 4
• D1 Farewell Felonious Fly: 5
• E How to Use this Text: 8
• THE APPETIZERS: 9
• Vectors and Kinematics: 11
• 112 The Forces of Business Meet the Forces of Nature: 15
• 113 Alaskan Cruise: 19
• 114 The Gorge Near George: 23
• 12 Vector Multiplication: 29
• 121 The Smoke Jumpers of Erehwon: 30
• 122 War Games of the Mind: 33
• 123 Flying by the Seat of Your Pants: 37
• 124 Mikes Train Ride: 42
• 13 Supplementary Recipes: 45
• A Rolling Wheel Gathers No Moss But: 46
• Torpedos Away: 47
• Feeling the Electric Force: 48
• Newtonian Mechanics: 49
• 211 Jack and Jill Go Up the Hill: 50
• 212 Will Jack Fall Down and Break His Crown?: 52
• 213 Mr Xs New Ride: 56
• 214 This Governor Is Not a Politician: 61
• 22 Energy and Momentum: 64
• 222 How Arthur Won the Nobel Prize: 69
• 223 A Heck of a Wreck: 73
• 224 G Forces: 75
• 23 Rotational Dynamics: 82
• 232 The Atwood Supreme: 87
• 233 Fast Freddies Trick Shot: 91
• 24 Supplementary Recipes: 97
• Suspension Bridge: 98
• A Sticky Encounter: 99
• Erehwon Space Probe Explosion: 100
• THE ENTREES: 101
• Vector Calculus: 103
• 312 Abigail Ant Roams the Beach Ball: 109
• 313 This Doughnut Isnt for Eating: 114
• 32 Vector Operators: 119
• 322 Are You Conservative Mr Vector Field?: 125
• 33 Supplementary Recipes: 131
• Alice in Cylinder Land: 132
• These Operators Have Many Identities: 133
• Designing Gabrielles Toy Box: 134
• Newtonian Dynamics I: 135
• 412 A Rolling Road: 138
• 413 Pushing the Envelope: 143
• 414 Benny Boffos Hole in One: 146
• 42 Positiondependent forces: 153
• 422 A Hard Springs Journey: 159
• 423 Wouldnt Mr Kepler Be Pleased: 165
• 424 The NotsoSimple Pendulum: 172
• 43 Supplementary Recipes: 176
• Dr No Lets Go: 177
• In Search of the Central Force Law: 178
• The Force of Love: 179
• The Hanging Chain: 180
• Newtonian Dynamics II: 181
• 512 Jane Rescues Tarzan: 185
• 513 The Route to Chaos: 188
• 514 Blowing in the Wind Monte Carlo Style: 194
• 52 Accelerated Reference Frames: 198
• 522 Falkland Fiasco: 201
• 53 Supplementary Recipes: 205
• Tug of War Math vs Physics: 206
• Kids Will Be Kids: 207
• Power Spectrum Driving Miss Duffing: 208
• THE DESSERTS: 209
• Lagrangian Hamiltonian Dynamics: 211
• 611 Rock in the Rim: 212
• 612 Airtrack Mechanics: 215
• 613 Can You Top This Nutation?: 219
• 614 This Double Pendulum is Dynamite: 224
• 62 Calculus of Variations: 227
• 621 Of Wine Goblets and Whisky Tumblers: 228
• 622 Suzy Spiders Speedy Strand: 231
• 63 Some Hamiltonian Examples: 236
• 632 Lots of Lissajous Figures: 240
• 633 The KAM Torus and Hamiltonian Chaos: 244
• 64 Supplementary Recipes: 250
• Coupled Pendulums: 251
• The FermiPastaUlam Problem: 252
• The Toda Potential: 253
• Suzy Spiders Alternate Route: 254
• Bibliography: 255
• Index: 257
• The Development of Oz and Mozart: 1
• Why Security Is Not a Separable Concern: 2
• Design Guidelines for a Secure Multiparadigm Programming Language: 21
• A Program Verification System Based on Oz: 41
• Higher Order Programming for Unordered Minds: 53
• Compiling Formal Specifications to Oz Programs: 66
• Deriving Acceptance Tests from Goal Requirements: 78
• Using Mozart for Visualizing AgentBased Simulations: 89
• Web Technologies for Mozart Applications: 103
• Overcoming the Multiplicity of Languages and Technologies for WebBased Development Using a Multiparadigm Approach: 113
• PeertoPeer Development Platform for Mozart: 125
• ThreadBased Mobility in Oz: 137
• A Fault Tolerant Abstraction for Transparent Distributed Programming: 149
• Building Conversational Agents in Oz: 161
• An NLP Application with a Multiparadigm Architecture: 175
• The XDG Grammar Development Kit: 188
• Solving CSP Including a Universal Quantification: 200
• Compositional Abstractions for Search Factories: 211
• Implementing SemiringBased Constraints Using Mozart: 224
• Playing the Minesweeper with Constraints: 251
• Using Constraint Programming for Reconfiguration of Electrical Power Distribution Networks: 263
• Design and Usage of a Music Composition Environment Based on the Oz Programming Model: 277
• Solving the Aircraft Sequencing Problem Using Concurrent Constraint Programming: 292
• A Practical Solution Incorporating Constraint Programming and Heuristics: 305
• An Interactive Tool for the Controlled Execution of an Automated Timetabling Constraint Engine: 317

Bibliographic information

• Title: Computer Algebra Recipes for Classical Mechanics, Volume 2; Computer Algebra Recipes for Classical Mechanics, George McGuire
• Authors: Richard H. Enns, George C. McGuire
• Edition: illustrated
• Publisher: Springer Science & Business Media, 2002
• ISBN: 0817642919, 9780817642914
• Length: 265 pages
• Subjects: Computers / Computer Science; Computers / Mathematical & Statistical Software; Computers / Programming / Algorithms; Mathematics / Algebra / General; Mathematics / Applied; Mathematics / Discrete Mathematics; Science / Mechanics / General