Classical Mechanics PHYS 2006 Tim Freegarde 2020 21

Classical Mechanics PHYS 2006 Tim Freegarde 2020 -21 Forum 10

Triatomic molecule • determine force on, hence acceleration of, each atom • seek harmonic solutions to where • set , and • solutions are roots of TRANSLATION SYMMETRIC ASYMMETRIC 2

The pianoforte a soundboard strings bridge b keyboard hammer escapement action MODES OF COUPLED MOTION log. P • strong coupling rapid decay log. P “PROMPT” “AFTERSOUND” time • strike strings together to produce almost pure s FORTE • weak coupling slow decay • strike one string - una corda - to produce equal superposition • reinforced “aftersound” is audible even when played softly PIANO time • strike strings together from opposite sides to produce almost pure a G Weinreich, Sci Am (Jan 1979) pp 94 -102 3

Quantum mechanical harmonic oscillator • energy of vibrational mode is quantized: • , A D O’Connell, Nature 464, 697 (2010) 4

Textbooks Fowles & Cassiday Analytical Mechanics ► good: right level comprehensive on rigid-body dynamics; fine examples Chow Classical Mechanics ► good: right approach; concise French & Ebison Introduction to Classical Mechanics ► quite good: right level, well paced Kibble & Berkshire Classical Mechanics ► good, concise Marion & Thornton Classical Dynamics Morin Intro to Class Mech ► more advanced ► looks good, concise Landau & Lifshitz Mechanics ► classic theoretical approach Feynman Lectures on Physics ► excellent introduction: put on your Christmas list! Acheson From Calculus to Chaos ► inspiring, supplementary reading 5

Classical Mechanics LINEAR MOTION OF SYSTEMS OF PARTICLES centre of mass Newton’s 2 nd law for bodies (internal forces cancel) rocket motion rotations and infinitessimal rotations ANGULAR MOTION angular velocity vector, angular momentum, torque parallel and perpendicular axis theorems rigid body rotation, moment of inertia, precession conservative forces, law of universal gravitation GRAVITATION & KEPLER’S LAWS 2 -body problem, reduced mass planetary orbits, Kepler’s laws energy, effective potential NON-INERTIAL REFERENCE FRAMES NORMAL MODES centrifugal and Coriolis terms Foucault’s pendulum, weather patterns coupled oscillators, normal modes boundary conditions, Eigenfrequencies 6

Exam tips • State, What, Identify, Express, • Find no derivation required • Explain, Describe, How • in words… • Derive, Prove, Show that, • Determine state assumptions, proceed logically. Indicate, Calculate, • Evaluate, • Estimate numbers, with clear assumptions • Sketch • as it says, with appropriate detail… 7

Exam tips DEGREE CLASSIFICATIONS • First class (70%) • Ability to extend or adapt standard derivations & manipulations to unseen problems • Demonstrate good insight & knowledge beyond course • 2: 1 material (60%) • Recall of standard derivations, manipulations & examples to discuss critically & demonstrate some insight • • 2: 2 Ability (50%) • Recall of simple derivations, manipulations & examples • Some ability to discuss critically • Third (40%) • Knowledge of basic definitions, formulae, phenomena & examples • Ability to apply formulae directly 8

Classical Mechanics A Merry Christmas to all Classical Mechanics! 9

Classical Mechanics PHYS 2006 Tim Freegarde