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C4CM
Section Five


Singularities
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23. Poincare Sections
24. Linear Algebra
25. Optimal Controls
26. Potential Theory
27. Envelope Curve
28. Vibrations
29. Time
30. Uncertainty
31. Quantum
Chemistry
32. Fractal Theory
TAB 32
Fractal Theory Logo
FRACTAL THEORY

There are a few unresolved issues: (1) how do the fractal levels intersect, (2) how do you go from the 3D Schrodinger Electron Cloud Plots to the 2D "galactic atom" and (3) what's the orientation of the coordinate system that organizes the fluxion accumulation that allegedly makes up the Fourier Series structure of Earth's gravity field. Amazingly, all three of these important questions are answered by a single illustration.


Resonance in the Mars Jupiter System


  1. The figure shows the intersection between the inner and outer planets - a fractal division according to the system wave. The intersection is stitched together by nested equilateral triangles, symptomatic of the 3BP.
  2. The coordinate systems between fractal levels are orthogonal, and oriented perpendicular to the axes of the stable equilibrium orbit triangles. In the case of the solar system, Earth's orbital plane crosses the symmetric plane on about Halloween (New Years Eve for pagans) and it crosses the invariant plane about three months later; the two lines of nodes are orthogonal, being separated by ninety degrees of heliocentric longitude.
  3. The 2D/3D transition is also by this fluxion coordinate system, shown in the 3D transfer from Earth to Mars by a spacecraft - not much of a projection above the plane of the page, but perhaps the first increment in the inclination direction for staged transitions.

Also consider the dramatic bending of the arcs for Earth, Mars, and the spacecraft. The illustration is scaled (via Fractal Theory) down to fit the sun at say Earth's orbit for the outer corona. This suggests the bending of light may be different for different planes of approach to the sun (e.g. the sun's gravity does not emanate uniformly in all directions, but only in a fraction of the whole sphere - the plane of the solar system - a very energy efficient mechanism). Applying fly by geometry to this situation, it suggests anomalies internal to the sun. Alternatively, this may be related to the wave/particle duality of light.

Notice how the colinear axes intersect at right angles. Perhaps halo orbits at a colinear points are inter level hinges, flexible bonds between successive dimensions (unstable in either dimension, but stable between them) and halo orbits around L1 and L3 are inter dimensional free return orbits. Perhaps L4/L5 points are "particles" and L1, L2, and L3 are "waves" in the non rotating system.


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© 2004 WH Clark