Classical Mechanics with Maple

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. 1 Introduction to Maple V.- 1.1 Basics.- 1.1.1 Entering Expressions.- 1.1.2 Fundamental Data Types.- 1.1.3 Basic Mathematical Functions.- 1.1.4 Variables.- 1.1.5 Sequences, Lists, and Sets.- 1.2 Algebraic Equations.- 1.3 Calculus and Differential Equations.- 1.3.1 Differentiation and Integration.- 1.3.2 Solving Differential Equations.- 1.3.3 Limits and Series.- 1.4 Simplification and Manipulation of Results.- 1.4.1 factor, expand, normal.- 1.4.2 collect, sort, coeff.- 1.4.3 combine.- 1.4.4 convert.- 1.5 Extending the Power of Maple.- 1.5.1 User-Defined Functions and Procedures.- 1.5.2 Access to the Maple Library.- 1.6 Graphics.- 1.7 Problems.- 2 Review of Introductory Mechanics.- 2.1 Kinematics in Rectangular Coordinate Systems.- 2.2 Newton’s Laws of Motion.- 2.3 Examples of Motion Under Constant Forces.- 2.3.1 Pulley and Incline System.- 2.3.2 Mass Sliding Down a Movable Incline.- 2.3.3 Force Applied to Stacked Boxes.- 2.3.4 Car Moving Around a Banked Curve.- 2.4 Conservation of Mechanical Energy.- 2.4.1 Motion of a Bead on a Wire.- 2.4.2 A Spring-Powered Cannon.- 2.5 Momentum Conservation.- 2.5.1 A Head-On Elastic Collision.- 2.5.2 The Ballistic Pendulum.- 2.5.3 A Collisional Party Trick.- 2.6 Problems.- 3 Newtonian Dynamics of Particles.- 3.1 Kinematics in Other Coordinate Systems.- 3.1.1 Polar Coordinates.- 3.1.2 Cylindrical Coordinates.- 3.1.3 Spherical Coordinates.- 3.2 Explicitly Time-Dependent Forces.- 3.3 Position- or Velocity-Dependent Forces.- 3.3.1 Projectile Motion with Air Resistance.- 3.3.2 Bead Sliding on a Rotating Rod.- 3.4 Work and Energy.- 3.4.1 Projectile Motion from an Energy Viewpoint.- 3.4.2 An Electrostatic Example.- 3.5 Power.- 3.5.1 Object Falling Through a Viscous Fluid.- 3.6 Angular Momentum and Torque.- 3.6.1 Circular Motion.- 3.7 Central Forces.- 3.7.1 Motional Constants Under Central Forces.- 3.7.2 Calculation of Orbits.- 3.8 Problems.- 4 The Harmonic Oscillator.- 4.1 Linear Restoring Force.- 4.2 Simple Harmonic Motion.- 4.2.1 Amplitude and Phase.- 4.2.2 Scaling of the Equation of Motion.- 4.2.3 Phase Plots.- 4.3 Damped Harmonic Motion.- 4.3.1 Equation of Motion and Its Solutions.- 4.3.2 Further Examination of the Underdamped Case.- 4.4 Sinusoidally-Driven Harmonic Motion.- 4.4.1 Solution of the Equation of Motion.- 4.4.2 Energy, Power, and Resonance.- 4.5 Impulse-Driven Harmonic Oscillator.- 4.6 Approximate Simple Harmonic Motion.- 4.6.1 The Simple Pendulum.- 4.6.2 Numerical Solution for the Simple Pendulum.- 4.7 Problems.- 5 Systems of Particles.- 5.1 The Two-Body Problem.- 5.2 The N-Body Problem.- 5.2.1 Momentum.- 5.2.2 Kinetic Energy.- 5.2.3 Angular Momentum.- 5.3 Simple Rigid Body Motion.- 5.3.1 Centers of Mass and Moments of Inertia.- 5.3.2 Yo-Yo on an Incline.- 5.3.3 Beetle on a Turntable.- 5.4 Equilibrium of a Rigid Body.- 5.5 Coupled Harmonic Oscillators.- 5.6 Problems.- References.