Classical mechanics overview [mln69]

Space and time -- Galilei's principle of relativity -- Newton's laws of dynamics [mln1]

Impact of symmetry [mln70]

Conservation laws [mln2]

Minimizing time of slide when friction is present [mex154]

On frozen pond [mex204]

The quick, the short, and the scenic [mex205]

When push comes to shove [mex206]

Spherical pendulum of varying length [mex226]

Dragging block by elastic cord [mex227]

Centripetal elevator [mex228]

Lateral force on hanging chain [mex231]

Solution by quadrature [mln4]

Phase portraits of conservative systems [msl5]

Potential energy of periodic motion reconstructed [mex232]

Solution by separation of variables [mln72]

Position-dependent acceleration [mex203]

Growth of falling raindrop [mex229]

Modeling attenuation [mex230]

Phase portrait: plane pendulum [msl8]

Velocity vector field in phase plane [mln109] *

Phase portrait: magnetic pendulum [msl9]

Classification of fixed points in plane [mln73]

Table of fixed points in 2D phase space [msl10]

Isoclines [mln31]

Limit cycles [mln74]

Feedback control [mln33]

Logistic model (continuous version) [mln32]

Continuous logistic model [mex107]

Summary of properties [mln14]

Holonomic constraints [mln36]

Example: disk rolling along incline [mln76]

Differential constraints [mln37]

Heading toward moving target [mex235]

Newtonian mechanics in the presence of holonomic constraints [mln5]

D'Alembert's principle [mln7]

Lagrange equations derived from D'Alembert's principle [mln8]

Simple applications of Lagrangian mechanics [mln77]

Pendulum with sliding pivot: Lagrange equations

Plane pendulum with periodically driven pivot II [mex249]

Plane pendulum with periodically driven pivot III [mex250]

Restoring force of elastic string [mex251]

Conservation laws and symmetry [mln11]

Routhian function [mln39]

Noether's theorem I [mln12]

Noether's theorem II [mln13]

Noether's theorem III [mln42]

Dissipative forces in Lagrangian mechanics [mln9]

Generalized forces of constraint in Lagrangian mechanics [mln15]

Variational problems with auxiliary conditions [mln16]

Isoperimetric problem

Geodesics [mln38]

Extremum principles [msl20] *

Generalized forces of constraint and Hamilton's principle [mln17]

Central force motion: one-body problem [mln67]

Central force problem: formal solution [mln18]

Orbits of power-law potentials [msl21] *

Virial theorem [mln68]

Changing orbit by brief rocket boost [mex163]

Kepler orbital equation [mex274] *

Bounded orbits open or closed [mln79]

Bertrand's theorem [mln44]

Stability of circular orbits [mex53]

Small oscillations of radial coordinate about circular orbit [mex125]

Angle between apsidal vectors for nearly circular orbits [mex126]

Robustness of apsidal angles [mex127]

Apsidal angle reinterpreted [mex128]

Apsidal angle at very high energies [mex129]

Apsidal angle at very low energies [mex130]

Orbits of Kepler problem [msl23]

Motion in time on elliptic orbit [mln19]

Close encounter of the first kind [mex145]

Kepler's second and third laws [mex43]

Circular and radial motion in inverse-square law potential [mex164]

Orbital differential equation [mln46]

Laplace-Runge-Lenz vector [mln45]

Precession of the perihelion [mln21]

Precession of the perihelion: orbital integral [mex165]

Precession of the perihelion: orbital differential equation [mex166]

Elliptic and hyperbolic orbits [mex169]

Determination of the scattering angle [mln20]

Scattering angle in the laboratory frame [msl3]

Elastic collision: angle between scattered particles [mex240]

Elastic collision: velocities of scattered particles [mex241]

Mechanical refraction [mex167]

Scattering from a spherical potential well [mex168]

Grazing collision between flat surfaces [mex219]

Absorption cross section of power-law potential [mex242]

Small-angle scattering [mln105]

Small-angle scattering from-power-law potential [mex246]

Classical inverse scattering [mln104]

Classical inverse scattering problem I [mex243]

Classical inverse scattering problem II [mex244]

Classical inverse scattering problem III [mex245]

Decay of particle I [mln102]

Decay of particle II [mln103]

Decay of particle: maximum kinetic energy [mex237]

Decay of particle: directions in lab frame I [mex238]

Decay of particle: directions in lab frame II [mex239]

What is vertical? [mex170]

Lagrange equations in rotating frame [mex171]

Holonomic constraints in rotating frame [mln23]

Parabolic slide on rotating Earth [mex172]

Rotational kinetic energy [mln25]

Kinetic energy of rolling cylinder [mex173]

Principal axes of inertia [mln80]

Simulating a stick by three point masses [mex143]

Angular momentum [mln26]

Eulerian angles of rotation [msl25]

Eulerian angular velocities [msl26]

Rotating rectangular box [mex174]

Euler's equations [mln27]

Heavy wheels [mex175]

Torque-free motion of asymmetric top [msl28]

Steady precession of symmetric top [mex176]

Heavy symmetric top: general solution [mln47]

Heavy symmetric top: steady precession [mln81]

Heavy symmetric top: precession and nutation [msl49]

Stability of sleeping top [mex177]

Rolling pendulum [mex178]

From sliding to rolling motion [mex220]

Rolling inhomogeneous disk [mex179]

Solid sphere rolling on plane [mln106]

Driven harmonic oscillator I [mln28]

Amplitude resonance and phase angle [msl48]

Driven harmonic oscillator: steady state solution [mex180]

Driven harmonic oscillator: kinetic and potential energy [mex181]

Driven harmonic oscillator: power input [mex182]

Quality factor of damped harmonic oscillator [mex183]

Driven harmonic oscillator II [mln29]

Fourier coefficients of a sawtooth force [mex184]

Fourier coefficients of periodic seuence of rectangular pulses [mex185]

Driven harmonic oscillator III [mln107]

Small oscillations [mln43]

Transformation to principal axes [mln30]

Elastic chain [mln48]

Blocks and springs in series [mex123]

Two coupled oscillators [mex186]

Three coupled oscillators [mex187]

What is the physical nature of these modes? [mex114]

Small oscillations of the double pendulum [mex124]

Hamiltonian and canonical equations [mln82]

Variational principle in phase space [mln83]

Properties of the Hamiltonian [mln87]

Use of cyclic coordinates in Lagrangian and Hamiltonian mechanics [mln84]

Velocity-dependent potential energy [mln85]

Charged particle in electromagnetic field [mln86]

Canonical transformations (of coordinates in phase space) [mln89]

Canonicity and volume preservation [mln90]

Infinitesimal canonical transformations [mln91]

Canonicity of time evolution: Liouville theorem [tln45], [tln46]

Actions and angles for librations [mln93]

Actions and angles for rotations [mln94]

Poisson brackets [msl30]

Specifications of Hamiltonian system [mln95]

Hamilton's characteristic function [mln97]

Dissipative dynamical systems [mln101]

Fixed points in 3D phase flow [msl16]

Limit cycles in 3D phase flow [msl17]

Toroidal attractor in 3D phase flow [msl18]

Strange attractor in 3D phase flow: Roessler band
[msl19]

Integrability as a universal property [mln98]

Integrability as a contingent property [mln99]

Poincaré surface of section [mln100]

Summary of properties [msl15]

Toda system (integrable) [msl12]

Henon-Heiles system (nonintegrable) [msl13]

Introduction to Hamiltonian chaos [mln108]

Relativity of space and time [mln50]

Relativity of simultaneity [mln51]

Time dilation paradox [mln52] *

Length contraction paradox [mln53]

Hello Earth [mex207]

Who passes more quickly? [mex208]

Time on the fly [mex236]

Pion decay in accelerator [mex209]

Interstellar travel [mex210]

TGV [mex211]

Minkowski diagram I: relativity of simultaneity [mln54]

Minkowski diagram II: length contraction and time dilation [mln55]

Twin paradox [mln56]

Longitudinal Doppler effect [mln57]

Optical birthday cards [mex212]

Two views of an event [mex213]

Hello Earth again [mex214]

Relative and absolute [mln59]

Lorentz transformation I [mex215]

Lorentz transformation II [mex216]

Observing transverse motion of meter stick [mln60]

Skater's paradox [mln61] *

Skate mail fallacy [mex217]

Interstellar speed control [mex218]

Mass and energy [mln62]

Relativistic momentum [mln63]

Momentum conservation [mex221]

Relativistic mass [mex222]

Relativistic energy I [mln64]

Relativistic energy II [mln65]

Photon rocket [mex223]

Photon absorption and photon emission [mex224] *

K meson decay [mex225]

**Some Relevant Textbooks**

- H. Goldstein:
*Classical Mechanics.*Addison Wesley, 1981. - I. Percival and D. Richards:
*Introduction to Dynamics.*Cambridge University Press, 1982. - L. D. Landau and E. M. Lifshitz:
*Mechanics.*Pergamon Press, 1976. - J. V. José and E. J. Saletan:
*Classical Dynamics: A Contemporary Approach.*Cambridge University Press, 1998. - J. L. McCauley:
*Classical Mechanics: Transformation, Flows, Integrable and Chaotic Dynamics.*Cambridge University Press, 1997. - D. T. Greenwood:
*Classical Dynamics*. Dover Publications 1997. - J. B. Kogut: Introduction to Relativity. Harcourt/Academic Press 2001.
- Friedhelm Kuypers: Klassische
Mechanik. Wiley-VCH 1997.

- V. I. Arnold:
*Mathematical Methods of Classical Mechanics.*Springer-Verlag, 1978. - A. J. Lichtenberg and M. A. Lieberman:
*Regular and Stochastic Motion.*Springer-Verlag, 1983. - R. C. Hilborn:
*Chaos and Nonlinear Dynamics. An Introduction for Scientists and Engineers.*2nd edition. Oxford University Press 2000. - R. C. Hilborn and N. B. Tufillaro (Eds.):
*Chaos and Nonlinear Dynamics.*(collection of reprinted articles) AAPT Publication, 1999. - M. Tabor:
*Chaos and Integrability in Nonlinear Dynamics - An Introduction.*Wiley, 1989. - R. H. Abraham and C. D. Shaw: Dynamics - The Geometry of Behavior. Aerial
Press, Santa Cruz 1984.

Do you have a question about any of the problems [mex]?

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Last updated 12/19/18