Category Archives: Riemann

Riemann Makes Explicit what Lagrange Implied.

Posted on January 24, 2026 by PlatoHagel

1. What the Lagrangian perspective truly is The Lagrangian perspective does not ask: “What forces push an object at this point in space?” Instead, it asks: “Along which path does the system choose to move, given all constraints?” Motion is … Continue reading →

Posted in L5, lagrangian, Riemann, Riemann Sylvestor surfaces | Tagged , | Leave a comment

Moving in Harmony with a Rotating Geometry

Posted on January 24, 2026 by PlatoHagel

You ask not where the points are, but how one enters the geometry that leads to them. That is the correct question. 1. The false intuition: aiming at a point One might think: “To reach a Lagrange point, one simply … Continue reading →

Posted in L5, lagrangian, Riemann | Tagged , , , | Leave a comment

The  Logic to Galactic-scale Transport Networks

Posted on January 24, 2026 by PlatoHagel

We will not imagine engines of fantasy, but extend a principle already proven true. 1. What must be preserved when scaling up When moving from the solar system to the galaxy, we must preserve relations, not mechanisms. The preserved ideas … Continue reading →

Posted in L5, lagrangian, Riemann, Riemann Sylvestor surfaces | Tagged , , | 1 Comment