Four Body Problem

An Approach to the Four Body Problem

by Frank C. Fung - 1st published in December, 2007.

This paper is published in honor of my father , the late Charles Hok-Ling Fung ( 1909-2002 ) , on the occassion of his 98th birthday on 2007-12-16 .

Summary & Brief Introduction :

The { Tetrahedron } is core and central to the { Four Body Problem } ,
- and 6 Degrees-Of-Freedom ( DOF's ) are usually involved in defining the { size and shape } of the { Tetrahedron } .
We noticed that the { line } joining the mid-points on each pair of { non-touching / opposite sides } always passes thru the { centroid } of the { Tetrahedron } ,
- and this set of { 3 lines } may then be used to fully define the 6-sided { Tetrahedron } .
The method of construction is as follows :
- Take 3 sticks of any arbitrary lengths and orient these in { 3-D space } so that :
  - the 3 sticks bisect one-another .
The { point-of-intersection } for the { 3 sticks } is then the { centroid } of the { Tetrahedron } , and :
- the 6 end-points on the { 3-sticks } then match exactly onto the 6 mid-points on the { 6 sides } .
This then fully defines { Tetrahedron } .
Hopefully , this will lead to a better understanding of the { Four Body Problem } , and further .

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	Links to other Sections
Section I	Setting up the Reference Frames
Section II	The 12 Degrees-Of-Freedom for the Tetrahedron
Section III	The 5 Categories of Tetrahedra
Section IV	Constructing the { General Tetrahedron }
Section V	The { Flattened Tetrahedron }
Section VI	Brief Summary on the Tetrahedron
Section VII	Setting up for Angular Momentum Issues
Section VIII	Cross-Product Considerations
Section IX	Concluding Remarks
Appendix A	A Numerical Example for the Cross-Product of 2 Tetrahedra

	Epilogs added 2008-1-07
Epilog I	An Elaboration on the Cross-Product [ T-on-T ]
Epilog II	On the { [ Zero ] Angular Momentum Vector }
Epilog III	On { Mirror / Rotated / Counter Images }

( Three Body Problem / Characteristics of Numbers / Matrix & Linear Algebra / 'I-CHING' / Triangle / Odd-On-Odd Format / Multiplication Table for Modulo P / Symmetry and Combinatorics / Solid Object with 14 Faces )

An Approach to the Four Body Problem

by Frank C. Fung - 1st published in December, 2007.

Top Of Page

This paper is published in honor of my father , the late Charles Hok-Ling Fung ( 1909-2002 ) , on the occassion of his 98th birthday on 2007-12-16 .

Summary & Brief Introduction :

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Original dated 2007-12-16 *** Updated 2008-1-07 / 11-01 / 2009-10-26