![]() ![]() Exponentiating r w for some scalar r that quantifies the “amount of rotation” will then produce an element of SO(2,1) that preserves n.įor example, an element of so(2,1) that annihilates n = e t + e x is: 0 One way to find a null rotation that preserves a given null vector n is to first find an element w of the Lie algebra so(2,1) that annihilates n. Exponentiate an element of the Lie algebra There are (at least) five ways to cook up a null rotation that preserves a given vector.ġ. Null rotations are Lorentz transformations that preserve a null vector, just as ordinary rotations preserve a timelike vector and boosts preserve a spacelike vector. Back to home page | Site Map | Side-bar Site Map.Symmetries and the 24-cell | Average Shadows | Ball Bearings in a Hypersphere | Black Hole Passing | Born Rigid Motion | Catacaustics | Resonant Modes of a Conical Cavity | The Doppler Shift Triangle Law | Conic Section Orbits | Double-Crossing Orbits | Dihedral Angles | The Ellipse and the Atom | Find The Fake Coin | The Finite Fall | General Relativity in 2+1 dimensions | Howell’s Moving Orbits | Klein's Quartic Curve | Paparazzo vs Bodyguards | Light Mill applet | Littlewood applet | LRL made easy | The Mermin-Peres Magic Square Game | There Are No Corkscrew Orbits | Peeling the Octonions | Ordered Sums | Optimised Origami | Weak-field GR near a planar mass | Polar Orbits Around Binary Stars | The Rindler Horizon | Rotating Elastic Rings, Disks and Hoops | Constant Weight Rollercoasters | Steffen’s Polyhedron | Superpermutations | Symmetric Waves | Symplectic applet | The Tell-Tale Board | Exact values of regular 10j symbols.If you link to this page, please use this URL:.Null Rotations in 2+1 dimensions - Greg Egan Null Rotations in 2+1 dimensions by Greg Egan ![]()
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