WebDefinition. In general terms, a smooth dynamical system is called hyperbolic if the tangent space over the asymptotic part of the phase space splits intotwo complementary directions, one which is contracted and the other which is expanded under the action of the system. In the classical, so‐calleduniformly hyperbolic case, the asymptotic part ... WebHyperbolas, which are closely related to the hyperbolic functions, also define the shape of the path a spaceship takes when it uses the "gravitational slingshot" effect to alter its course via a planet's gravitational pull propelling it away from that planet at high velocity. The spaceship traces out a hyperbola as it uses the "slingshot" effect.
Hyperbolic Geometry Brilliant Math & Science Wiki
Webnoun Mathematics. a function of an angle expressed as a relationship between the distances from a point on a hyperbola to the origin and to the coordinate axes, as … Webhyperbolic geometry, also called Lobachevskian Geometry, a non-Euclidean geometry that rejects the validity of Euclid’s fifth, the “parallel,” postulate. Simply stated, this Euclidean … aws s3 アクセスキー シークレットキー 確認
Hyperbolic Definition & Meaning - Merriam-Webster
Web17 mrt. 2024 · It is this geometry that is called hyperbolic geometry. Spherical geometry From early times, people noticed that the shortest distance between two points on Earth were great circle routes. For example, the Greek astronomer Ptolemy wrote in Geography (c. 150 ce ): Get a Britannica Premium subscription and gain access to exclusive content. WebThe hyperbolic functions are periodic w.r.t. the imaginary component with period 2πi for sinh, cosh, sech & cosech; and with period πi for tanh and coth. Hyperbolic functions in the complex plane. z representing a complex number, the functions sinh z and cosh z are said to be holomorphic or analytic (see below figures). Web20 dec. 2024 · The hyperbolic functions are a set of functions that have many applications to mathematics, physics, and engineering. Among many other applications, they are used to describe the formation of satellite rings around planets, to describe the shape of a rope hanging from two points, and have application to the theory of special relativity. aws s3 アクセス 制限