Activities - Modern Classical Mechanics

Every unit of the course opens with an activity notebook — a hands-on simulation or thought experiment, worked in Python, that motivates the formal notes that follow. These aren’t optional extras; they’re where most of the actual modeling happens. Below is the full set, grouped by topic, plus the homework sets that apply them.

Unit activities¶

Unit	Activity	What you’ll do
1	Overture: What is Classical Physics?	Survey where classical mechanics shows up in current research and industry.
2	Computing as a tool for science	Use the Euler method to discretize Newton’s second law and step a trajectory forward numerically.
3	What is Mathematical Modeling?	Build a model of a physical system from assumptions to equations.
4	Why does fluid drag complicate things?	Add drag to the equations of motion and see how it changes a trajectory.
5	Conservation Laws	Track energy through a simulation and check where it is (and isn’t) conserved.
6	Stability and Equilibria	Find equilibrium points and test whether small perturbations grow or decay.
7	Nonlinear Dynamics	Plot phase portraits for nonlinear first-order ODEs and locate critical points.
8	Oscillations	Model a simple oscillator and compare the numerical solution to the analytic one.
9	Driven Oscillators and Resonance	Drive an oscillator at different frequencies and find the resonance peak.
10	Chaotic Dynamics	Use `scipy.integrate.solve_ivp` to simulate a damped, driven pendulum and look for sensitivity to initial conditions.
11	Calculus of Variations	Explore what it means for a path to minimize a functional.
12	The Principle of Least Action	Derive equations of motion from stationary action instead of forces.
13	Lagrangian Mechanics	Apply the Lagrangian formulation to a system with constraints.

Each activity has a matching notes notebook with the formal derivation — for example, Unit 10’s notes work through the same damped driven pendulum in more depth.

Homework¶

Eight problem sets apply each unit’s tools to new systems: Homework 1, 2, 3, 4, 5, 6, 7, and 8.

Adding an activity¶

Activities live as MyST Markdown notebooks in content/notebooks/. To add one:

Add a new .md file there, following the style of an existing *_start.md notebook (a motivating question or system, then Python code cells that simulate or explore it).
Register it in the project.toc list in myst.yml so it appears in the site navigation.
Open a pull request on the GitHub repository.