The 2nd Rule of Motion: Straight or Circle

Rule 2: Straight or Circular

Every moving identity moves in a straight line when alone, and in a curve or a circle when moving with others. When in a circle, it moves away from the center.

This leads to spin and vortex rotation, producing fractal patterns.

This gives the equations:

1. No vortex: d²r / dt² = 0
2. Within a vortex: d²r / dt² = −Ω × (Ω × r) − 2Ω × dr / dt

This captures Descartes’ three clauses: straight line alone, curve/circle with others, and (in the rotating frame) the striving away from the center via a_cf.

This is taken from:

• Principia Philosophia Part 2 Article 33
• Principles of Cartesian Philosophy Part 2 Proposition 7