published: true
description: "Can position and changing inertia alone determine motion? The NKT Law introduces two intuitive products that model dynamic systems with surprising clarity."
tags: physics, sciencetech, programming, simulation, openscience
"I did not invent it. I only wrote down what nature has been doing for billions of years."
— Nguyễn Khánh Tùng
In physics, Newton’s second law is treated as a bedrock. But as developers, we know: even the most solid APIs can have edge cases. What if classical mechanics missed a few?
This post introduces the NKT Law — a lightweight, two-variable model that captures system motion with variable inertia. Surprisingly, it works — and is based on just two products.
🧠 The Core Idea
Instead of building around F = ma, the NKT Law models motion trends using two expressions:
-
S1 = x * p→ Position-Momentum product -
S2 = (dm/dt) * p→ Mass-Change-Momentum product
Where:
-
x: displacement from equilibrium -
p: linear momentum (mass * velocity) -
dm/dt: rate of mass change over time
🎯 Interpretation
These two values tell us if a system is moving toward or away from equilibrium:
-
S1 > 0: Divergence (system is moving away) -
S1 < 0: Convergence (system returning) -
S2 > 0: Mass change reinforces motion (e.g. thrust) -
S2 < 0: Mass change resists motion (e.g. drag)
They apply to rockets, harmonic oscillators, or even planetary motion. And yes — they work with real-world data.
📈 Developer-Friendly Form
If you want to simulate a system, you only need:
js
const p = mass * velocity;
const s1 = position * p;
const s2 = massChangeRate * p;
if (s1 > 0) system.diverging = true;
if (s2 < 0) system.losingMomentum = true;
It’s as easy to plug into a simulation as a PID controller.
🔭 Why Developers Should Care
Easy to code into physics engines
Minimalistic — only needs x, v, m, and dm/dt
Can model real-world systems like rockets, fluid tanks, or object aggregation
Think of it as a physics middleware — minimal input, clear behavioral output.
🚀 Real-World Examples
The NKT Law has been tested with:
🚀 Rocket launch: S2 > 0 during fuel burn
🌍 Earth’s orbit: S1 flips at perihelion/aphelion
🌀 Oscillators: S1 sign flip matches turning points
Graphs and case studies are included in the full paper (linked below).
🧪 Want to Try It?
🔗 Full paper on Figshare
🌐 Wikiversity summary
🧮 Want sample code or JS sim? Let me know in the comments.
🙌 Final Thoughts
The NKT Law isn’t a replacement for Newton — it’s an extension.
A new lens. A new minimal model.
It’s not about complexity. It’s about pattern clarity.
If you're building physics engines, simulations, or just love modeling elegant systems — this is worth a look.
Sometimes, nature’s logic is easier to code than we think.
📩 Contact: traiphieu.com@gmail.com
🧠 Author: Nguyễn Khánh Tùng
📘 ORCID: 0009-0002-9877-4137
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