platonic orbits and fully democratic satellite networks

15
Platonic Orbits and Fully Democratic Satellite Networks Latham Boyle (w/ Kendrick Smith) (Earlier work by G. Mozhaev and J. G. Walker, 1970’s)

Upload: lorant

Post on 22-Feb-2016

50 views

Category:

Documents


0 download

DESCRIPTION

Platonic Orbits and Fully Democratic Satellite Networks. Latham Boyle ( w / Kendrick Smith). (Earlier work by G. Mozhaev and J. G. Walker, 1970’s). A Regular Tetrahedral Orbit?. Point Groups in 3D. Point Groups in 3D. Point Groups in 3D. Point Groups in 3D. Point Groups in 3D. - PowerPoint PPT Presentation

TRANSCRIPT

Page 1: Platonic Orbits and  Fully Democratic Satellite Networks

Platonic Orbitsand

Fully Democratic Satellite Networks

Latham Boyle (w/ Kendrick Smith)

(Earlier work by G. Mozhaev and J. G. Walker, 1970’s)

Page 2: Platonic Orbits and  Fully Democratic Satellite Networks
Page 3: Platonic Orbits and  Fully Democratic Satellite Networks
Page 4: Platonic Orbits and  Fully Democratic Satellite Networks

A Regular Tetrahedral Orbit?

Page 5: Platonic Orbits and  Fully Democratic Satellite Networks
Page 6: Platonic Orbits and  Fully Democratic Satellite Networks

Point Groups in 3D

Page 7: Platonic Orbits and  Fully Democratic Satellite Networks

Point Groups in 3D

Page 8: Platonic Orbits and  Fully Democratic Satellite Networks

Point Groups in 3D

Page 9: Platonic Orbits and  Fully Democratic Satellite Networks

Point Groups in 3D

Page 10: Platonic Orbits and  Fully Democratic Satellite Networks

Point Groups in 3D

Page 11: Platonic Orbits and  Fully Democratic Satellite Networks
Page 12: Platonic Orbits and  Fully Democratic Satellite Networks
Page 13: Platonic Orbits and  Fully Democratic Satellite Networks
Page 14: Platonic Orbits and  Fully Democratic Satellite Networks

More generally:

• Classic problem in mathematics: Given a space (especially a maximally symmetric space like the sphere, the plane, the hyperboloid) in a given dimension, and with a given signature, what are the possible STATIC lattices/tilings?

Page 15: Platonic Orbits and  Fully Democratic Satellite Networks

More generally:

• Classic problem in mathematics: Given a space (especially a maximally symmetric space like the sphere, the plane, the hyperboloid) in a given dimension, and with a given signature, what are the possible STATIC lattices/tilings?

• New problem: Given a space (especially a maximally symmetric) in a given dimension, and with a given signature, what are the possible DYNAMICAL lattices/tilings?