Simulating a 2D Quadcopter from Scratch lands a compact, executable tutorial

Overview

It has been reported that a new tutorial, shared via Hacker News and linked to a personal blog, walks readers through building a 2D (planar) quadcopter simulation from first principles — deriving Newton‑Euler equations, converting them to state‑space form, and implementing the dynamics in Python. The post is clear and hands‑on: start with a free‑body diagram, pick y (horizontal) and z (vertical) axes, define the rotation φ, and then grind through the trig until the forces and torque reveal themselves. Short answer: you get a minimal model you can run on your laptop. Why bother? Because a good simulator is the foundation for controller design and reinforcement learning. No magic. Just math and code.

Under the hood

The writeup resolves two thrusts F1 and F2 into y/z components and writes the three rigid‑body equations: two translational and one rotational. The author then defines inputs u1 = F1+F2 and u2 = F1−F2 and a six‑dimensional state x = [y, z, φ, ẏ, ż, φ̇]ᵀ to produce a first‑order system ẋ = f(x,u). Example physical values appear in the code: m = 0.8 kg, g = 9.81 m/s², l = 0.5 m, I = 1e‑3 kg·m², with a compact dynamics() function written in NumPy. It’s tidy, readable, and runnable — the kind of tutorial that gets you from pen‑and‑paper derivation to simulated trajectories without a lot of hand‑waving.

Why it matters

A simple 2D quadcopter model is a pragmatic first step. Want to design an LQR, test PID gains, or train an RL agent? Start here. It strips away messy aerodynamics and prop‑wash details so you can feel the dynamics under your feet — or rather, under the simulated propellers. The emotional payoff is real: deriving the equations yourself makes the control problems that follow less spooky. And while the model is deliberately minimal, it’s easy to extend toward 3D and richer physics if you need to go full‑flight‑sim.

Short and sweet: if you’re learning controls or prototyping algorithms for drones, this is well worth a look. It’s practical, educational, and executable — a neat example of “learn by doing” for engineers and researchers alike.

Sources: mrandri19.github.io, Hacker News