machwerk-relational-lab-newton

This repository implements a relational formulation of Newtonian two-body mechanics using the Machwerk TRD formal core.

It provides a computational and structural framework for expressing classical gravitational dynamics in relational form. The focus is on structural invariants, energy relations, and stability analysis within established classical mechanics.

Reference: Crawerimer, Machwerk Relational Physics. Zenodo DOI: https://doi.org/10.5281/zenodo.18478523

Purpose

The objective of this repository is to demonstrate that classical Newtonian dynamics can be formulated and analyzed through a relational TRD structure. The implementation provides a relational construction of the two-body gravitational system, a structural expression of energy conservation, a stability analysis of bound orbital configurations, and explicit equivalence to standard Newtonian results.

Conceptual Basis

A physical system is represented as a relational triple (TRD) of dynamically coupled quantities. For the Newtonian two-body system this is expressed as TRD(m1, m2, r). The dynamical behavior is derived from structural relations between these quantities rather than from coordinate embedding.

Repository Structure

This repository will contain core relational implementation modules, analytical derivations in document form, minimal computational examples, and structural consistency tests.

Scope

This lab operates strictly within classical mechanics and serves as a stable relational test environment for further formal development.
Usage

Run locally with Python 3:

python3 test_energy_conservation.py
python3 relational_analysis.py
python3 relational_orbit_scan.py

These scripts verify structural consistency, scaling behavior, and energy relations within the relational TRD embedding of Newtonian mechanics.