Classical Mechanics with Maple

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.