One-Parameter Group
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High Quality Content by WIKIPEDIA articles! In physics, one-parameter groups describe dynamical systems. Furthermore, whenever a system of physical laws admits a one-parameter group of differentiable symmetries, then there is a conserved quantity, by Noether's theorem. In special relativity an appeal is made to the rapidity parameter to compare inertial frames of reference. The rapidity replaces the velocity in kinematics and dynamics of relativity theory. Since rapidity is unbounded, the one-parameter group it stands upon is non-compact. The rapidity concept was introduced by E.T. Whittaker…mehr

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High Quality Content by WIKIPEDIA articles! In physics, one-parameter groups describe dynamical systems. Furthermore, whenever a system of physical laws admits a one-parameter group of differentiable symmetries, then there is a conserved quantity, by Noether's theorem. In special relativity an appeal is made to the rapidity parameter to compare inertial frames of reference. The rapidity replaces the velocity in kinematics and dynamics of relativity theory. Since rapidity is unbounded, the one-parameter group it stands upon is non-compact. The rapidity concept was introduced by E.T. Whittaker in 1910, and named by Alfred Robb the next year. The rapidity parameter amounts to the length of a hyperbolic versor, a concept of the nineteenth century. Mathematical physicists James Cockle, William Kingdon Clifford, and Alexander Macfarlane had all employed in their writings an equivalent mapping of the Cartesian plane by operator (cosh a + r sinh a), where a is the hyperbolic versor parameter and rr = +1.