Course Name: Techniques of Theoretical Mechanics

Course Number: PH 335

Year/Term: 2025
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

W 9/24 Day 1

Welcome

Establish Classroom Norms

Welcome to PH 335!

APS Teamwork Guidelines

Key Request Form
Gradescope Guides for Students

Photo Release Form

Consent to Participate in Research

Research Consent Form

Th 9/25 Day 2 MathBits

Power Series

Adding Functions Pointwise
Using Technology to Explore Power Series Approximations
Guess the Power Series
Derivation of Power Series Coefficients
Calculating Coefficients for a Power Series

Video: Intro to Power Series
GMM: Definition of Power Series
GMM: Guessing Power Series from Graphs
GMM: Common Power Series
GMM: Calculating Power Series Coefficients
GMM: Discussion of Approximations using Power Series
GMM: Dimensions in Power Series

F 9/26 Day 3 MathBits

More Power Series

Visualization of Power Series Approximations
Power Series Theorems

GMM: Theorems about Power Series

GMM: Convergence of Power Series

Hyperbola Trig Functions

Geometry of Hyperbola Trig

Lorentz Transformation (Geometric)

Dray 4.1, 4.2, & 4.3, Lorentz Transform

M 9/29 Day 4 MathBits

Polar Coordinates Review

GMM: Polar Coordinates

Circle Trig

Clock Trigonometry

Dray Ch.3,

GMM: Polar and Rectangular Coordinates
GMM: Visualizing Circle Trigonometry
Webpage: Review Trig Functions
Simulation: Trig Tour PhET

Cylindrical & Spherical Coordinates

Curvilinear Coordinates Introduction
Surfaces with constant curvilinear coordinates

GMM: Curvilinear Coordinates
GMM: Change of Coordinates
GEM 1.4

Generalized Coordinates & Degrees of Freedom

Taylor 7.3

T 9/30 Day 5 MathBits

Partial Derivatives

GMM: Review of Single Variable Differentiation
GMM: Leibniz vs. Newton

Zapping with "d"

Zapping with d (Lecture)
Practice Zapping with d

GMM: Differentials
GMM: Rules for Differentials
GMM: Properties of Differentials
GMM: Substitution
GMM: Differentials: Summary

First-Order ODEs: Forms & Theorems

GMM: First-Order ODEs: Forms and Theorems

Separable ODE's

GMM: Separable ODEs

W 10/1 Day 6 MathBits

Vectors

Representations of Vectors
Properties of Abstract Vector Spaces

GMM: Vectors
GMM: Bases
GMM: Unit Vectors

Matrix Elements as Dot Products

Generalization of the Dot Product to an Inner Product of Finite Vectors
Matrix Addition \& Multiplication
Finding Matrix Elements

GMM: Matrix Addition
GMM: Scalar Multiplication
GMM: Matrix Multiplication
GMM: Transpose
GMM: Hermitian Adjoint

Components of Vectors in Multiple Coordinate Systems

Describing a Vector with 2 Different Coordinate Systems
Which Way is North?
Which Way is North? [AIMS]

Dot Product

Dot Product Review
Visualizing the Dot Product
Visualizing the Dot Product in Higher Dimensions

GMM: The Dot Product
GMM: Visualizing the Dot Product

Th 10/2 Day 7 MathBits

Calculating the Distance Between Two Points

The Distance Formula (Star Trek)

GMM: The Distance Formula
GEM 1.1.2, 1.1.4

Vectors in Different Coordinate Systems

Describing a Vector with 2 Different Coordinate Systems
Curvilinear Basis Vectors

GMM: Polar Basis Vectors
GMM: Orthonormality of Basis Vectors

Dot Product in Curvlinear Coordinates

Dot Product in Curvilinear Coordinates
Representations for Finding Components

GMM: Orthonormal Basis Vectors

F 10/3 Day 8 MathBits

The Spacetime Interval

M 10/6 Day 9

Galilean & Special Relativity

Galilean Spacetime Diagrams
Linear Acceleration

Dray Ch.1, 2.2; GLA 2.3, Surveyor's Parable

YouTube Video: Matrix Multiplication

YouTube Video: Galilean Relativity

Sensemaking: Functional Behavior

Postulates of Special Relativity

Dray 2.2, Taylor 15.3

Video: Postulates of Special Relativity

T 10/7 Day 10

Simultaneous Events

Dray 2.2

YouTube Video: Simultaneity

Time Dilation

Time Dilation
Possible Worldlines

Dray 2.3, Taylor 15.3, 15.4

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

Sensemaking: Special Case Analysis

W 10/8 Day 11

Length Contraction

Length Contraction Derivation

Day 2.3, Taylor 15.5,

YouTube Video: Relativity Animation

HW 3 w/Solution

Th 10/9 Day 12

Lorentz Transformations

Lorentz Transformation (Algebraic)

Dray 2.4, Taylor 15.1, 15.6

Sensemaking: "What kind of a 'beast' is it?"

F 10/10 Day 13

Barn & Pole Paradox

Paradoxes I

Dray 5.1, 5.2, 5.3, Ch. 6

T 10/14 Day 15

Simultaneous and Colocated Events

Prep Events on Spacetime Diagrams

Invariant Scalar Product

Right Angles on Spacetime Diagrams

Velocity Addition

Taylor 15.7, Dray 6.2

Video: Derivation of Relativistic Velocity Equation

W 10/15 Day 16

Relativistic Energy & Momentum

Taylor 15.12, 15.13, 15.14; Dray Ch. 9

Relativistic Collisions

Mass is not Conserved

M 10/20 Day 19

Big Quiz

Review Newton's 2nd Law

Taylor 1.4, 1.6

Video: Brief Review of Newton's 2nd Law

T 10/21 Day 20

Prep: Intro to Lagrangian Mechanics

Prep: Principle of Least Action, Derivation of the Euler-Lagrange Equation, Interpreting the Euler-Lagrange Equation (this last one is the most important)

Taylor 7.1, 7.2, 7.4

Video of Class

Lagrangian Examples

Near-Earth Projectile with Lagrangians

Taylor 7.5, 7.6, 7.7

W 10/22 Day 21

Prep: Basis Vectors

Prep: Basis Vectors, Time Derivatives of Polar Basis Vectors

GSF 4.1, GSF 4.9

Video of Class

More Lagrangian Examples

Particle Confined to a Cylinder

Th 10/23 Day 22

Homework Due at noon

F 10/24 Day 23

More Lagrangian Examples

Lengthening Spherical Pendulum

Taylor 3.4, 3.5

Video of Class

M 10/27 Day 24

Prep: Acceleration in Polar Coordinates

Acceleration in Polar Coordinates

Video of Class

More Lagrangian Examples

Box Sliding Down Frictionless Wedge

T 10/28 Day 25

Continue Box on Frictionless Wedge

Video of Class

Rolling without Slipping

Ball Rolling down a Curved Ramp

Intro to Hamiltonian Mechanics

Taylor 7.8, 13.1, 13.2

Extras: Intro to Hamiltonians

Interpreting Hamiltonian Functions

Hamiltonian Examples

Taylor 13.3, 13.4

W 10/29 Day 26

Intro to Drag Force

Taylor 2.1, Intro to Drag in a Fluid Lecture

Video of Class

Linear Drag

Projectile with Linear Drag

Th 10/30 Day 27

Quadratic Drag

Taylor 2.4

F 10/31 Day 28

Course Review

HW 10 w/Solution

HW 2

Homework

HW 3

Homework

HW 4

Homework

HW 5

Homework

HW 8

Homework

HW 9

Homework

HW 10

Homework