Exercises in Classical Mechanics with Applications
Porter Johnson

Here is a list of descriptive titles of the exercises in the book, as arranged by Chapter

Chapter I
•   1.1  Geodesics on a Cylinder
•   1.2  Geometrical Optics
•   1.3  Geometrical Optics, Continued
•   1.4  Uniformly Loaded Cable
•   1.5  String Hanging over Table
•   1.6  Falling Chain
•   1.7  Area of Inscribed Rectangle
•   1.8  Minimum Area under Curve
•   1.9  Rotating Bucket as Parabolic Mirror
• 1.10  Geodesics on a Cone
• 1.11  Meniscus
• 1.12  Capillary Action
• 1.13  Particle Moving Freely on Surface of Sphere
• 1.14  Navigation across a Flowing River

Chapter II
•   2.1  Rayleigh Equation
•   2.2  Abel Integral Equation
•   2.3  Linear Air Resistance
•   2.4  Elliptic Integrals
•   2.5  Rocket Motion
•   2.6  Period from Potential
•   2.7  Air Resistance
•   2.8  Period of Negative Energy Bound States
•   2.9  Bounded Motion
• 2.10  Cubic Potential
• 2.11  Inverse Problem
• 2.12  Capstan
• 2.13  Conveyer Belt
• 2.14  Small Vibration
• 2.15  Double Well Duffing Equation
• 2.16  Two Center Repulsion
• 2.17  Energy Independent Period
• 2.18  Stirling's Formula
• 2.19  Random Walks and the Levy Arc Sine Law
• 2.20  Simple Model with Limit Cycle

Chapter III
•   3.1  Trajectory of Hit Baseball
•   3.2  Trajectory of Pitched Baseball
•   3.3  Mass Sliding on Sphere
•   3.4  Determination of Potential
•   3.5  Trajectory for Repulsive Inverse Square Potential
•   3.6  Two Mass Pendulum
•   3.7  Stick and Massless Rod
•   3.8  Stick and Two Springs
•   3.9  Spring Pendulum
• 3.10  Virial Theorem
• 3.11  Fibonacci Numbers and Golden Mean
• 3.12  Stability of Circular Orbits
• 3.13  Central Force Motion
• 3.14  Frahm Vibration Absorber
• 3.15  Stability of Circular Motion
• 3.16  Particle Suspended by Two Springs

Chapter IV
•   4.1  Yo-yo Problem
•   4.2  Mass Sliding on Moving Slab
•   4.3  Plank Sliding off Wall
•   4.4  Planar Rigid Body
•   4.5  Bowling Ball
•   4.6  Two Masses and Spring
•   4.7  Flywheel Governor
•   4.8  Sweet Spot of Baseball Bat
•   4.9  Billiards
• 4.10  Sphere Rolling on Fixed Sphere
• 4.11  Moments of Inertia of cones
• 4.12  Small Oscillations of Pivoted Curved Bar
• 4.13  Rod Suspended by Spring
• 4.14  Chasles Theorem
• 4.15  Anisotropic Oscillator on Sphere

Chapter V
•   5.1  Coriolis Deflection of Projectile
•   5.2  Space Elevator
•   5.3  Ball on Table
•   5.4  Bead on Rotating Circular Wire
•   5.5  Falling Raindrop
•   5.6  Bead on Rotating Parabolic Wife
•   5.7  Collapsing Floor
•   5.8  Rotating Spring
•   5.9  Pivoted Falling Stick
• 5.10  Uniform Rotation of Foucault Pendulum
• 5.11  Ball Rolling on Rotating Turntable
• 5.12  Bounce of Rotating Ball
• 5.13  Ball Sliding on Rotating Bent Wire
• 5.14  Projectile Drift
• 5.15  Rotating Wire
• 5.16  Pendulum on Rotating Ring
• 5.17  Mass being Lowered by Crane
• 5.18  Rotating Pendulum

Chapter VI
•   6.1  Determination of Potential from Trajectory
•   6.2  Inverse Squared Deviation from Newtonian Gravity
•   6.3  Tunnelling through the Earth
•   6.4  Time of Flight
•   6.5  Roche's Limit
•   6.6  Detection of Planets
•   6.7  Orbital Velocity Distribution
•   6.8  Asteroid Jumping
•   6.9  Astronaut Releases Object
• 6.10  Poynting-Robertson Effect
• 6.11  Bertrand's Theorem on Closed Orbits
• 6.12  Planetary Orbits from Symmetry
• 6.13  Motion near Stable Lagrange Point
• 6.14  Satellite Orbiting Oblate Planet
• 6.15  Exploding Star in Binary System
• 6.16  Planet between Two Stars

Chapter VII
•   7.1  Totally Inelastic Collision with elastic Zeno Balls
•   7.2  Additional Zeno Ball Collision
•   7.3  Scaling of Cross Section for 1 / r n Potential
•   7.4  Square Well Potential
•   7.5  Gravitational Capture
•   7.6  Capture Cross Section for r - 4  Potential
•   7.7  Inverse Scattering Problem
•   7.8  Cross Section
•   7.9  Time Delay
• 7.10  Rutherford Scattering
• 7.11  Scattering from Hard Ellipsoid of Revolution
• 7.12  Rocket Approaching Planet
• 7.13  Scattering from Inverse Sixth Power Potential

Chapter VIII
•   8.1  Poisson Brackets
•   8.2  Constant Force Hamilton-Jacobi Equation
•   8.3  Hamilton-Jacobi Equation with Time-Dependent Force
•   8.4  Inverse Hyperbolic Cosine Potential
•   8.5  Planar Motion in a Central Potential
•   8.6  Time Dependent Harmonic Oscillator
•   8.7  Action Variables with Attractive Coulomb Potential
•   8.8  Mass Sliding Inside Cone
•   8.9  Hamiltonian with Damping
• 8.10  Maupertuis Principle
• 8.11  Hamilton-Jacobi Equation in Parabolic Coordinates
• 8.12  Two Center Gravitational Force
• 8.13  Motion along a Cycloid
• 8.14  Relativistic Confinement
• 8.15  Foucault Pendulum in Action-Angle Variables
• 8.16  Dipole Potential

Chapter IX
•   9.1   Hadamard's Determinant Inequality
•   9.2  Hill Determinant
•   9.3  Botafumeiro
•   9.4  Verhulst Model of Population Control
•   9.5  Fish Population
•   9.6  Lanchester's Law of Combat Strength
•   9.7  Predator-Prey Populations
•   9.8  Integral Henon-Heiles System
•   9.9  Brusselator Oscillating Chemical Reactions
• 9.10  Epidemic Model of Kernack-McKendrick
• 9.11  Damped Driven Duffing Oscillator
• 9.12  Model for Arms Race
• 9.13  Lotka-Volterra System
• 9.14  Swinging Atwood's Machine

Chapter X
• 10.1    Eigenvalues of Loaded String
• 10.2    Equivalence of D'Alembert Solution to Eq.(10.8)
• 10.3    Mass on String
• 10.4    Suspended String
• 10.5    Travelling Waves on Long String
• 10.6    Heavy Spring
• 10.7    String in Viscous Medium
• 10.8    Rotating String
• 10.9    Driven String
• 10.10  Rotating Loop
• 10.11  Space Charge
• 10.12  Composite String
• 10.13  Plucked String
• 10.14  String with Ring Attached

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