# Classical Mechanics with Maple

Springer Science & Business Media, Oct 23, 2000 - Science - 174 pages
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 Copyright