Maths for (Games) Programmers Section 7 - SpaceTime

Special Relativity
Introduction
Minkowski and Hestenes SpaceTimes
Minkowski SpaceTime   Â3.1     Minkowski TimeSpace Â1.3     Nullvector Decomposition     Alternative spacetime representations     Points as Events     Time dilation     Length contraction     Lorentzian vs Einsteinian Relativity     Composition of relative velocities     Proper Time
Picturing Minkowski Geometry
Planes and Simplexes     Simultaneity and Chronological ordering     Impossibility of FTL Signalling
Spacetime Multivectors
Hyperbolic Spinor Representation of 1-vectors     Canonical Rotor Form of Even Spacetime Multivectors     Canonical Exponentiated Form of Even Spacetime Mutivectors     Â4.2 Genralised Homegenised Minkowski Spacetime     Â5.2 Spacially Extended GHMST
k-spheres and Nullcones
Nullcones     Dirac D Function     Tspheres and Tballs
Helices
Timelike Helix     Null Helix     Spacelike Helix - Timelike Drift     Spacelike Helix - Spacelike Drift     Spacelike Helix - Null Drift

Spacetime Kinematics and Mechanics
Energy and Momentum     Justifying E=mc2     DeBroglie Waves
Relativistic Fluid Mechanics
Spacetime 1-flows     Current     Probability Flows     Multiflows     Mobiles

Multivector Potential Theory
0-potentials
Newton Potential     Effective Potential     Orbital Stability Indicator     Stability Indicators of a Klein Gordan 0-Potential     Circular Orbits      Quantised Orbits     Ring Potential     Morse Potential     Born Mayer Potential     Lennard-Jones Potential     Tangential occlusion potential     Yukawa potential     Trigonometric Potential     Logarithmic Potential
1-potentials
Bivector Force Fields     Path tsphere Intersections     Propagated Lienard-Wiechart Potential     Field due to straight worldine     Instananeous Field due to helical worldine     Averaged Field due to helical worldine
Self Interaction
Timelike self interaction of null helix     Null self interaction of spacelike helix     Constructing the potential
Useful zero-divergent 1-fields
Hyperbolic Gaussian Wave Packets
Choosing The Normalisation Constant

General Relativity
Notations
Material-energy 1-tensor in a flat space
Gravitation as a higher dimensional embedding
Flat N-D spacetime     Point Embedding     Metric Tensor     Covariant Coordinates     Parallel Transport     Geodesics and Velocity     Coderivative
Material-energy 1-tensor in a curved space
Slow Flows
Curvature 2-Tensor
Einstein 1-Tensor
GR Field Equation
Newtonian approximation
Yilmaz Gravitation
Schwarschild Solution
References/Source Material for Multivector Relativity

Glossary   Contents   Author
Copyright (c) Ian C G Bell 1998, 2014
Web Source: www.iancgbell.clara.net/maths
Latest Edit: 15 Jun 2014.