For example, one can learn about the Poincar?half-plane model of hyperbolic geometry through a development based on hyperbolic motions.
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It also plays an important role in hyperbolic geometry, where the Poincar?half-plane model provides a way of examining hyperbolic motions.
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He noted that when r, y, z are variable and \ varphi is constant, they describe the worldline of a charged body in hyperbolic motion.
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To distinguish the hyperbolic motions, a particular line or circle is taken as the connected components, and hyperbolic motions must " not " permute these components.
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To distinguish the hyperbolic motions, a particular line or circle is taken as the connected components, and hyperbolic motions must " not " permute these components.
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It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram.
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1910 : Arnold Sommerfeld brought Born's formulas for hyperbolic motion in a more concise form with l = ict as the imaginary time variable and \ varphi as an imaginary angle:
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1909 : Max Born denotes the motion with constant magnitude of Minkowski's acceleration vector as " hyperbolic motion " ( ), in the course of his study of rigidly accelerated motion.
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From the perspective of an onboard observer, the crew will feel a gravitational field opposite the engine's acceleration, and the universe ahead will appear to fall in that field, undergoing hyperbolic motion.
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Hyperbolic motions are often taken from inversive geometry : these are mappings composed of reflections in a line or a circle ( or in a hyperplane or a hypersphere for hyperbolic spaces of more than two dimensions ).
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