Techniques of Theoretical Mechanics | 2021-Fall

Course Name
Techniques of Theoretical Mechanics
Course Number
ph335
Year/Term
Fall-2021
Course Credits
4
Class meeting times
9 hours of lecture/discussion per week for 5 weeks.
Prerequisites
PH 212 and MTH 254
Course description
Newtonian, Lagrangian, and Hamiltonian classical mechanics. Special relativity with relativistic mechanics.
Topic/Day
Activities
Resources
Homework Due
Day 1
Welcome

Gradescope Help

Request a Key to Wngr 304f (you may list me as the supervisor)

Establish Classroom Norms
APS Teamwork Guidelines
Day 2
Galilean Relativity
Practice Galilean Boost

Prep: Matrix Multiplication

Support Reading Dray Ch.1, 2.2; GLA 2.3

Postulates of Special Relativity
Support Reading Dray 2.2, Taylor 15.3, Surveyor's Parable
Homework Due
Day 3
Time Dilation
Possible Worldlines

Support Reading Dray 2.3, Taylor 15.3, 15.4

Time Dilation Animation (1:10-5:38)

Sensemaking: Special Case Analysis
Length Contraction

Support Reading Day 2.3, Taylor 15.5,

Relativity Animation

Day 4
Finish Length Contraction
Lorentz Transformations
Support Reading Dray 2.4, Taylor 15.1, 15.6
Simultaneous Events
Events on Spacetime Diagrams
Support Reading Dray 2.2
Homework Due
HW 2
HW 2 (pdf)
Day 5
Barn & Pole Paradox
Pole and Barn Paradox
Support Reading Dray 5.1, 5.2, 5.3, Ch.6
Day 6
Practice with Spacetime Diagrams
The invariant spacetime interval
Homework Due
HW 3
HW 3 (pdf)
Day 7
Velocity Addition
Support Reading Taylor 15.7, Dray 6.2
Practice Inner Products
Practice Inner Products (pdf)
Circle Trig

Prep: Trig Tour Phet

Support Reading Dray Ch.3,

Geometry of Hyperbola Trig
Support Reading Dray 4.1, 4.2, & 4.3, Lorentz Transform
Right Angles on Spacetime Diagrams
Day 8
Invariant Scalar Product
Practice Hyperbola Trig
Relativistic 2-Velocity
Homework Due
HW 4
HW 4 (pdf)
Relativistic Energy & Momentum
Support Reading Taylor 15.12, 15.13, 15.14; Dray Ch. 9
Day 9
Day 10
Relativistic Collisions
10/27 Wed
Homework Due
HW 5
HW 5 (pdf)
Day 11
Midterm
Day 12
Zapping with "d"
Practice Zapping with d (w/ Solution)
Practice Zapping with d (pdf)
Practice Separable ODEs (w/ Solution)
Practice Separable ODEs (pdf)
Separable ODE's
Review Newton's 2nd Law
Support Reading Taylor 1.4, 1.6
Day 13
Intro to Drag Force
Support Reading Taylor 2.1
Linear Drag
Projectile with Linear Drag
Homework Due
HW 6
HW 6 (pdf)
Day 14
Power Series
Support Reading GMM 7.1, 7.3
Practice Power Series (w/ Solution)
Practice Power Series (pdf)
Quadratic Drag
Support Reading Taylor 2.4
Hyperbola Trig Functions
Support Reading Taylor Problem 2.33
Homework Due
HW 7
HW 7 (pdf)
Day 15
Intro to Lagrangian Mechanics
Support Reading Taylor 7.1, 7.2, 7.4
Generalized Coordinates & Degrees of Freedom
Support Reading Taylor 7.3
Lagrangian Examples
Support Reading Taylor 7.5, 7.6, 7.7
Homework Due
HW 8
HW 8 (pdf)
Day 16
More Lagrangian Examples
Curvilinear Coordinates Practice (w/ Solution)
Curvilinear Coordinates Practice (pdf)
Practice Acceleration in Polar Coordinates (w/ Solution)
Practice Acceleration in Polar Coordinates (pdf)
Basis Vectors
Support Reading GSF 4.1, GSF 4.9
Acceleration in Polar Coordinates
More Lagrangian Examples
Sphere Rolling Down an Incline
Day 17
More Lagrangian Examples
Box Sliding Down Frictionless Wedge
Noether's Theorem & Conserved Quantities
Day 18
Intro to Hamiltonian Mechanics
Support Reading Taylor 7.8, 13.1, 13.2
Hamiltonian Examples
Support Reading Taylor 13.3, 13.4
Homework Due
HW 9
HW 9 (pdf)
Day 19
Course Review
Homework Due
HW 10
HW 10 (pdf)
Final Exam
More Lagrangian Examples
Prep: Simultaneous and Colocated Events
Spacetime interval
Rolling without Slipping
More Lagrangian Examples
Support Reading Taylor 3.4, 3.5