Classical Mechanics with Maple

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Springer Science & Business Media, Oct 23, 2000 - Science - 174 pages
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Many problems in classical mechanics can now be readily solved using computers. This text integrates Maple, a general-purpose symbolic computation program, into the traditional sophomore- or junior-level mechanics course. Intended primarily as a supplement to a standard text, it discusses all the topics usually covered in the course and shows how to solve problems using Maple and how to display solutions graphically to gain further insight. The text is self-contained and can also be used for self-study or as the primary text in a mechanics course.
 

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Contents

Introduction to Maple V
iv
111 Entering Expressions
v
112 Fundamental Data Types
3
113 Basic Mathematical Functions
4
114 Variables
6
115 Sequences Lists and Sets
8
12 Algebraic Equations
9
13 Calculus and Differential Equations
13
342 An Electrostatic Example
88
35 Power
93
351 Object Falling Through a Viscous Fluid
94
36 Angular Momentum and Torque
95
361 Circular Motion
97
37 Central Forces
98
372 Calculation of Orbits
99
38 Problems
103

132 Solving Differential Equations
15
133 Limits and Series
18
141 factor expand normal
19
142 collect sort coeff
20
143 combine
22
15 Extending the Power of Maple
23
152 Access to the Maple Library
26
16 Graphics
27
17 Problems
31
Review of Introductory Mechanics
35
22 Newtons Laws of Motion
38
23 Examples of Motion Under Constant Forces
39
231 Pulley and Incline System
40
232 Mass Sliding Down a Movable Incline
43
233 Force Applied to Stacked Boxes
46
234 Car Moving Around a Banked Curve
51
24 Conservation of Mechanical Energy
53
242 A SpringPowered Cannon
56
25 Momentum Conservation
59
252 The Ballistic Pendulum
60
253 A Collisional Party Trick
61
26 Problems
65
Newtonian Dynamics of Particles
69
312 Cylindrical Coordinates
72
32 Explicitly TimeDependent Forces
73
33 Position or VelocityDependent Forces
76
332 Bead Sliding on a Rotating Rod
84
34 Work and Energy
86
The Harmonic Oscillator
107
42 Simple Harmonic Motion
108
421 Amplitude and Phase
109
422 Scaling of the Equation of Motion
110
423 Phase Plots
113
43 Damped Harmonic Motion
114
432 Further Examination of the Underdamped Case
118
44 SinusoidallyDriven Harmonic Motion
120
442 Energy Power and Resonance
122
45 ImpulseDriven Harmonic Oscillator
126
46 Approximate Simple Harmonic Motion
131
462 Numerical Solution for the Simple Pendulum
135
47 Problems
139
Systems of Particles
141
52 The NBody Problem
142
521 Momentum
143
522 Kinetic Energy
144
53 Simple Rigid Body Motion
145
531 Centers of Mass and Moments of Inertia
146
532 YoYo on an Incline
149
533 Beetle on a Turntable
152
54 Equilibrium of a Rigid Body
154
55 Coupled Harmonic Oscillators
157
56 Problems
163
References
167
Index
169
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