The 3rd Rule of Motion: Straight or Circle

Introductory Part

Table of Contents

The 3rd Rule says:

When a weaker identity hits a stronger, it will be deflected. When a stronger hits a weaker, it will transfer some of its force to the weaker.

$m_A\Delta v_A = -m_B\Delta v_B$ , $\ \alpha=\dfrac{S_B}{S_A+S_B}$ , $\ S=(m,\sigma,\rho)$

Symbol	Meaning
$A$ , $B$	labels for the two identities in the collision (identity A and identity B)
$m_A$ , $m_B$	mass of A, mass of B respectively
$v_A$ , $v_B$	velocity of A, velocity of B
$\Delta v_A$ , $\Delta v_B$	the change in velocity of A, and of B, caused by the collision
$=-$	the negative sign — B’s change is equal in size but opposite in direction to A’s
$\alpha$	(Greek letter alpha) the deflection fraction — how much A bounces off rather than pushes through
$S_A$ , $S_B$	the total “strength” of A and of B (defined below) — used to figure out who deflects and who transfers force
$S$	the strength vector itself — a bundle of three separate numbers, not just one
$m$ (inside $S$ )	the mass/material component of strength (physical size, military size, raw resources)
$\sigma$	(Greek letter sigma) the resolve/moral-cohesion component of strength (how determined or unified the side is)
$\rho$	(Greek letter rho) the persistence component of strength (staying power — economic endurance, cultural durability, ability to keep going)

Equation Meaning: whatever velocity change A undergoes, B undergoes the exact opposite — but which side actually bounces versus pushes through is decided by comparing their strength $S$ , and strength itself isn’t one number, it’s three things (mass, resolve, persistence) bundled together.

The 3rd Rule of Motion: Straight or Circle

mAΔvA=−mBΔvBm_A\Delta v_A = -m_B\Delta v_B , α=SBSA+SB\ \alpha=\dfrac{S_B}{S_A+S_B} , S=(m,σ,ρ)\ S=(m,\sigma,\rho)

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$m_A\Delta v_A = -m_B\Delta v_B$ , $\ \alpha=\dfrac{S_B}{S_A+S_B}$ , $\ S=(m,\sigma,\rho)$