Chapter 1. The Equations of Motion
§5 The Lagrangian for a system of particles
Chapter 2. Conservation Laws
§7 Momentum
§8 Centre of mass
§9 Angular momentum
- Problem 1 Angular momentum in cylindrical co-ordinates
- Problem 2 Angular momentum in spherical co-ordinates
- Problem 3 Conserved momenta in symmetric fields
§10 Mechanical similarity
Chapter 3. Integration of the Equations of Motion
§11 Motion in one dimension
- Problem 1 Pendulum period as a function of amplitude
- Problem 2 Period versus energy in three potential wells
§13 The reduced mass
§14 Motion in a central field
- Problem 1 Spherical pendulum
- Problem 2 Particle on the surface of a vertical cone
- Problem 3 Integrating the sliding-support pendulum
§15 Kepler's problem
Chapter 4. Collisions Between Particles
§16 Disintegration of particles
- Problem 1 Laboratory angles after a disintegration
- Problem 2 Lab angular distribution of decay products
- Problem 3 Range of angles between two decay products
§17 Elastic collisions
§18 Scattering
- Problem 1 Scattering by a perfectly rigid sphere
- Problem 2 Rigid-sphere cross-section vs. energy loss
- Problem 3 Power-law fields: cross-section vs. velocity
- Problem 4 Fall to the centre in an inverse-square field
- Problem 5 Fall to the centre in a field −α/rⁿ, n > 2
- Problem 6 Capture by a gravitating sphere
- Problem 7 Repulsive field from cross-section (Firsov)
§19 Rutherford's formula
§20 Small-angle scattering
Chapter 5. Small Oscillations
§21 Free oscillations in one dimension
- Problem 1 Amplitude and phase from initial conditions
- Problem 2 Frequencies of isotopic diatomic molecules
- Problem 3 Particle on a line held by a spring
- Problem 4 Particle on a circle held by a spring
- Problem 5 Small oscillations, sliding-support pendulum
- Problem 6 Tautochrone: period independent of amplitude
§22 Forced oscillations
- Problem 1 Forced oscillations under four forms of force Not done
- Problem 2 Final amplitude after a ramped-up force Not done
- Problem 3 Final amplitude after a constant force pulse Not done
- Problem 4 Amplitude after a linearly growing force Not done
- Problem 5 Amplitude after one period of a sine force Not done
§23 Oscillations of systems with more than one degree of freedom
- Problem 1 Two identical coupled oscillators Not done
- Problem 2 Oscillations of a coplanar double pendulum Not done
- Problem 3 Path of a space oscillator Not done
§24 Vibrations of molecules
- Problem 1 Symmetric linear triatomic molecule modes Not done
- Problem 2 Vibrations of a triangular triatomic molecule Not done
- Problem 3 Unsymmetrical linear triatomic molecule modes Not done
§26 Forced oscillations under friction
§27 Parametric resonance
- Problem 1 Second-order instability limits near γ = 2ω₀ Not done
- Problem 2 Region of instability near γ = ω₀ Not done
- Problem 3 Parametric resonance with a vibrating pivot Not done
§29 Resonance in non-linear oscillations
§30 Motion in a rapidly oscillating field
Chapter 6. Motion of a Rigid Body
§32 The inertia tensor
- Problem 1 Principal moments of inertia of molecules
- Problem 2 Moments of inertia of homogeneous bodies Not done
- Problem 3 Frequency of a compound pendulum Not done
- Problem 4 Kinetic energy of two hinged rods Not done
- Problem 5 Unbalanced rolling cylinder: kinetic energy Not done
- Problem 6 Cylinder inside a cylinder: kinetic energy Not done
- Problem 7 Kinetic energy of a cone rolling on a plane Not done
- Problem 8 Rolling cone, horizontal axis: kinetic energy Not done
- Problem 9 Ellipsoid, perpendicular axes: kinetic energy Not done
- Problem 10 Ellipsoid, two inclined axes: kinetic energy Not done
§35 Eulerian angles
- Problem 1 Heavy symmetrical top reduced to quadratures Not done
- Problem 2 Stability of a top spinning upright Not done
- Problem 3 Motion of a fast top Not done
§37 The asymmetrical top
- Problem 1 Free rotation of a top near a principal axis Not done
- Problem 2 Free asymmetrical top with M² = 2EI₂ Not done
§38 Rigid bodies in contact
- Problem 1 Rolling sphere by d'Alembert's principle Not done
- Problem 2 Rod against a wall held by a string Not done
- Problem 3 Rod between two planes held by two strings Not done
- Problem 4 Reactions in two hinged rods tied by a string Not done
§39 Motion in a non-inertial frame of reference
Chapter 7. The Canonical Equations
§40 Hamilton's equations
- Problem 1 Hamiltonian in three co-ordinate systems
- Problem 2 Hamiltonian in a uniformly rotating frame
- Problem 3 Hamiltonian of one heavy and n particles
§41 The Routhian
§42 Poisson brackets
- Problem 1 Poisson brackets: momentum, angular momentum
- Problem 2 Poisson brackets of angular momentum
- Problem 3 Bracket of a spherically symmetric φ with Mz
- Problem 4 Bracket of a vector function with Mz
§44 Maupertuis' principle
§48 Separation of the variables
- Problem 1 Hamilton–Jacobi: Coulomb plus uniform field Not done
- Problem 2 Hamilton–Jacobi for two fixed Coulomb centres Not done
§50 Canonical variables
§51 Accuracy of conservation of the adiabatic invariant
- Problem 1 Adiabatic invariant change for smooth ω(t) Not done
- Problem 2 Energy of an oscillator under weak friction Not done