Cumulative Lecture Notes

Feigenbaum on the Logistic Map

Introduction to Classical Chaos by Oriol Bohigas and Marie-Joya Giannonni

Excerpts from Classical Dynamics by J.V. Jose and E.J, Saletan

09-05-2007/L1, Historical Perspective, Lagrangian

[p1] [p2] [p3] [p4] [p5]

09-07-2007/L2, Galilean Invariance, Lagrangian of a Free Particle

[p6a] [p6] [p7]

09-10-2007/L3, System of Particles, Examples, Integrals of Motion, Energy

[p8a] [p9] [p10] [p11]

09-12-2007/L4, Momentum, Center of Mass, Angular Momentum, Cyclic Coordinates

[p12a] [p12] [p13] [p14] [p15] [p16] [p17]

09-17-2007/L5, Noether's Theorem, Constraints

[p16] [p17] [p18]

09-19-2007/L6, Constraint Forces, Euler Lagrange Equations with Constraints, Examples, Motion in One Dimension

[p19] [p20] [p21] [p22] [p23]

09-21-2007/L7, Motion in One Dimension, Reduced Mass, Motion in a Central Field

[p24a] [p24] [p25] [p26] [p27]

09-24-2007/L8, Bertrand-Koenig Theorem, Reason for Closed Orbit

[p28] [p29]

09-26-2007/L9, Bertrand-Koenig Theorem, Kepler Orbits

[p30a] [p30] [p31] [p32] [p33]

09-28-2007/L10, Collisions, Cross Section, Scattering in Central Potential

[p34a] [p34] [p35]

10-01-2007/L11, Rutherford Formula, Small Angle Scattering

[p36] [p37] [p38]

10-03-2007/L12, General Theory of Small Oscillations

[p39] [p40] [p41]

10-05-2007/L13, Coupled Oscillators

[p41a] [p42]

10-08-2007/L14, Parametric Resonances

[p43a] [p43] [p44]

10-10-2007/L15, Parametric Resonances, Anharmonic Oscillator

[p45] [p46] [p47]

10-12-2007/L16, Perturbation Theory of the Anharmonic Oscillator, Rotation Group

[p48a] [p48] [p49]

10-12-2007/L17, Perturbation Theory of the Anharmonic Oscillator, Rotation Group

[p50] [p51] [p52] [p53] [p54]

10-17-2007/L18, Rigid Body Motion, Inertia Tensor

[p55a] [p55] [p56] [p57]

10-19-2007/L19, Angular Momentum, Torque

[p58] [p59] [p60]

10-22-2007/L20, Euler Angles

[p61a] [p61] [p62] [p63]

10-24-2007/L21, Euler Angles, Euler Equations

[p64a] [p64] [p65] [p66]

10-26-2007/L22, Midterm:

List of Formulas is at the Bottom of the Page

10-29-2007/L23, Asymmetric Top, Nonintertial Frames

[p67a] [p67] [p68]

10-31-2007/l24, Noninertial Frames, Hamilton Equations, Poisson Brackets

[p69a] [p69] [p70]

11-02-2007/L25, Poisson Brackets, Hamilton's Principle, Maupertuis Principle

[p71a] [p71] [p72] [p73]

11-05-2007/L26, Canonical Transformations

[p74a] [p74] [p75] [p76] [p77] [p78]

11-07-2007/L27, Invariance of Poisson Brackets under Canonical Transformation

[p79] [p80] [p81]

11-09-2007/L28, Hamilton-Jacobi Theory, Separtion of Variables

[p82a] [p82] [p83] [p84] [p85]

11-12-2007/29, Example, Eletrocmagnetic Fields

[p86] [p87] [p88]

11-14-2007/L30, Liouville Theorem, Poincare Invariants

[p89a] [p89] [p90] [p91]

11-16-2007/L31, Poincare Sections

[p91a] [p91b] [p92] [p93] [p94]

11-19-2007/L32, Action-Angle Variables, Motion on Tori

[p95a] [p95] [p96] [p97] [p98]

11-21-2007/L33, Poincare Map, Area Preserving Maps, Cat Map

[p99a] [p99] [p100] [p101] [p102]

11-26-2007/L34, Kicked Rotor, Standard Map

[p103] [p104] [p105] [p106] [p107]

11-28-2007/L35, Classification of Systems, Poincare Recurrence Theorem
(Figures on pages 108bcd are from Saletan and Jose, Classical Dynamics)

[p108a] [p108b] [p108c] [p108d] [p108] [p109]

11-30-2007/L36, The Logistic Map

[p110] [p111] [p112] [p113]

12-03-2007/L37, Adiabatic Invariants

[p114] [p115] [p116]

12-05-2007/L38, Canonical Perturbation Theory

[p117] [p118] [p119]

12-07-2007/L39, Resonances in Perturbation Theory

[p120] [p120] [p121]

12-10-2007/L40, Poincare-Birkhoff Theorem, Homoclinic Tangle

[p122a] [p122] [p123] [p124]

12-12-2007/L41, Homoclinic Tangle, KAM Theorem

[p125] [p126] [p127] [p128] [p129] [p130]

12-14-2007/L42, Quantum Chaos

12-19-2007: Final Exam, 8.00-10.30 in P112

List of Formulas: [1] [2] [3] [4] [5] [6]

Jacobus Verbaarschot
Last revised: August 27, 2007.