Computer Algebra Recipes for Classical Mechanics

by Enns, Richard H.; McGuire, George

• ISBN13: 9780817642914
• ISBN10: 0817642919
• Edition: CD
• Format: Paperback
• Copyright: 2003-01-01
• Publisher: Birkhauser

Summary

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. For the reader's convenience, all recipes have been placed on a Windows Platform CD-ROM that comes with the book; MAC and UNIX systems are also compatible. The CD-ROM also includes computer algebra solutions to hundreds of problems.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.

Table of Contents

Preface	vii
Introduction	1	(1)
Computer Algebra Systems	1	(1)
The Spiral Approach to Learning Mechanics	2	(1)
Maple Help	3	(1)
Introductory Recipe	4	(4)
Farewell Felonious Fly	5	(3)
How to Use this Text	8	(1)
I THE APPETIZERS	9	(92)
Vectors and Kinematics	11	(38)
Vector Addition	11	(18)
Bogey 5	11	(4)
The Forces of Business Meet the Forces of Nature	15	(4)
Alaskan Cruise	19	(4)
The Gorge Near George	23	(6)
Vector Multiplication	29	(16)
The Smoke Jumpers of Erehwon	30	(3)
War Games of the Mind	33	(4)
Flying by the Seat of Your Pants	37	(5)
Mike's Train Ride	42	(3)
Supplementary Recipes	45	(4)
Bogey 5 Revisited	45	(1)
A Rolling Wheel Gathers No Moss, But...	46	(1)
Flight of Brunhilda Bumblebee	46	(1)
Colleen Better Beware	46	(1)
Justine's Clever Throw	46	(1)
Torpedos Away!	47	(1)
Mike's Vector Brain Teaser	47	(1)
Jennifer's Vector Identity Assignment	47	(1)
The Learnu Molecule	47	(1)
Feeling the Electric Force	48	(1)
Mike's Potpourri of Unit Vectors	48	(1)
Closest Possible Encounter	48	(1)
Envelope of Safety	48	(1)
Avoiding a Mortar Shell	48	(1)
Newtonian Mechanics	49	(52)
Motion Involving Constant Forces	49	(15)
Jack and Jill Go Up the Hill	50	(2)
Will Jack Fall Down and Break His Crown?	52	(4)
Mr. X's New Ride	56	(5)
This Governor Is Not a Politician	61	(3)
Energy and Momentum	64	(18)
Amazing But True	64	(5)
How Arthur Won the Nobel Prize	69	(4)
A Heck of a Wreck	73	(2)
G Forces	75	(7)
Rotational Dynamics	82	(15)
The Case of the Falling Pencil	82	(5)
The Atwood Supreme	87	(4)
Fast Freddie's Trick Shot	91	(6)
Supplementary Recipes	97	(4)
Gabrielle's Toy Car	97	(1)
Mike's Race	97	(1)
The Dirty Bird Window Washer	97	(1)
Suspension Bridge	98	(1)
Erehwonese Serving Platter	98	(1)
A Sticky Encounter	99	(1)
Rockets Away	99	(1)
Erehwon Space Probe Explosion	100	(1)
Gabrielle's Slippery Blocks	100	(1)
Another Toybox Problem	100	(1)
II THE ENTREES	101	(108)
Vector Calculus	103	(32)
Curvilinear Coordinates	103	(16)
The Case of the Artistic Slug	103	(6)
Abigail Ant Roams the Beach Ball	109	(5)
This Doughnut Isn't for Eating	114	(5)
Vector Operators	119	(12)
Enon on the Hill	119	(6)
Are You Conservative, Mr. Vector Field?	125	(6)
Supplementary Recipes	131	(4)
Bertie Bumblebee Leaves His B and B	131	(1)
Alice in Cylinder Land	132	(1)
Car Racing in the Great White North	132	(1)
The Making of Another Conservative Field	132	(1)
More Divs and Curls	132	(1)
These Operators Have Many Identities	133	(1)
Thoughts on Flux, From Heraclitas to Gauss	133	(1)
Felonious Fly (Jr.) Flees	133	(1)
Designing Gabrielle's Toy Box	134	(1)
Newtonian Dynamics I	135	(46)
Velocity-dependent forces	135	(18)
Justine Takes a Dive	135	(3)
A Rolling Road	138	(5)
Pushing the Envelope	143	(3)
Benny Boffo's Hole in One	146	(7)
Position-dependent forces	153	(23)
Mike's Mobile Modes	153	(6)
A ``Hard'' Spring's Journey	159	(6)
Wouldn't Mr. Kepler Be Pleased	165	(7)
The Not-so-Simple Pendulum	172	(4)
Supplementary Recipes	176	(5)
Nonlinear Drag on Trout Lake	176	(1)
More Golf, Anyone?	176	(1)
Dr. No Lets Go	177	(1)
George's Linear Inchworm	177	(1)
Period of an Anharmonic Oscillator	177	(1)
In Search of the Central Force Law	178	(1)
Orbital Precession	178	(1)
A Perturbing Solution	178	(1)
The Force of Love	179	(1)
Lord of the Rings?	179	(1)
The Growing Raindrop	179	(1)
The Hanging Chain	180	(1)
Nonlinear Drag on Trout Lake Revisited	180	(1)
Newtonian Dynamics II	181	(28)
Time-dependent forces	181	(17)
Mr. Q Feels the Lorentz Force	181	(4)
Jane Rescues Tarzan	185	(3)
The Route to Chaos	188	(6)
Blowing in the Wind, Monte Carlo Style	194	(4)
Accelerated Reference Frames	198	(7)
Merry-go-round Merriment	198	(3)
Falkland Fiasco	201	(4)
Supplementary Recipes	205	(4)
Will Ellen be Yellin'?	205	(1)
Poincare Sections and Strange Attractors	205	(1)
Tug of War: Math vs. Physics	206	(1)
Statistical Approach to Blowing in the Wind	206	(1)
Kids Will Be Kids	207	(1)
Falkland Fiasco, Revisited	207	(1)
Power Spectrum: The Idea	207	(1)
Power Spectrum: Driving Miss Duffing	208	(1)
Rocket Sled	208	(1)
III THE DESSERTS	209	(46)
Lagrangian & Hamiltonian Dynamics	211	(44)
Some Lagrangian Examples	211	(16)
Rock in the Rim	212	(3)
Airtrack Mechanics	215	(4)
Can You Top This Nutation?	219	(5)
This Double Pendulum is ``Dynamite''	224	(3)
Calculus of Variations	227	(9)
Of Wine Goblets and Whisky Tumblers	228	(3)
Suzy Spider's Speedy Strand	231	(5)
Some Hamiltonian Examples	236	(14)
Turning a Bar of Soap into a Conical Pendulum	236	(4)
Lots of Lissajous Figures	240	(4)
The KAM Torus and Hamiltonian Chaos	244	(6)
Supplementary Recipes	250	(5)
Parametric Excitation	250	(1)
The Oscillating Spherical Pendulum Ride	250	(1)
Coupled Pendulums	251	(1)
Eulerian Angles	251	(1)
George's Nonlinear Inchworm	251	(1)
The Fermi-Pasta-Ulam Problem	252	(1)
The Rotating Pendulum	252	(1)
The Toda Potential	253	(1)
Abby Moves in Great Circles	253	(1)
Suzy Spider's Alternate Route	254	(1)
Fermat's Principle and the Bending of Light	254	(1)
Bibliography	255	(2)
Index	257