Sierpinski (<1K)Maths for (Games) Programmers
Section 7 - SpaceTime

Special Relativity
    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
          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
          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
          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
          Zero-gradient 1-fields
    Hyperbolic Gaussian Wave Packets
          Choosing The Normalisation Constant

General Relativity
    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
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Latest Edit: 15 Jun 2014.