Course Name: Techniques of Theoretical Mechanics

Course Number: PH 335

Year/Term: 2021
Display other available years here.

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

Ph335 Intro

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

Galilean Relativity Lecture
Galilean Spacetime Diagrams
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

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

Length Contraction Derivation

Support Reading Day 2.3, Taylor 15.5,

Relativity Animation

Day 4

Finish Length Contraction

Lorentz Transformations

Lorentz Transformation (Algebraic)
Practice Lorentz Transformation

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

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

Tell a Story about a Spacetime Diagram
Draw the Spacetime Diagram that Matches the Story

The invariant spacetime interval

Homework Due

HW 3

Day 7

Velocity Addition

Support Reading Taylor 15.7, Dray 6.2

Practice Inner Products

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

Relativistic Energy & Momentum

Support Reading Taylor 15.12, 15.13, 15.14; Dray Ch. 9

Day 10

Relativistic Collisions

Mass is not Conserved

10/27 Wed

Homework Due

HW 5

Day 11

Midterm

Day 12

Zapping with "d"

Practice Zapping with d w/Solution
Practice Separable ODEs w/Solution

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

Day 14

Power Series

Calculating Coefficients for a Power Series
Visualization of Power Series Approximations

Support Reading GMM 7.1, 7.3

Practice Power Series w/Solution

Quadratic Drag

Support Reading Taylor 2.4

Hyperbola Trig Functions

Support Reading Taylor Problem 2.33

Homework Due

HW 7

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

Near-Earth Projectile with Lagrangians

Support Reading Taylor 7.5, 7.6, 7.7

Homework Due

HW 8

Day 16

More Lagrangian Examples

Lengthening Plane Pendulum

Curvilinear Coordinates Practice w/Solution
Practice Acceleration in Polar Coordinates w/Solution

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

Day 19

Course Review

Homework Due

HW 10

Final Exam

More Lagrangian Examples

Particle Confined to a Cylinder

Prep: Simultaneous and Colocated Events

Linear Acceleration

Spacetime interval

Pole and Barn: Interval

Rolling without Slipping

Ball Rolling down a Curved Ramp

More Lagrangian Examples

Lengthening Spherical Pendulum

Support Reading Taylor 3.4, 3.5