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By Gravesa W. G., Peckhamb B., Pastorc J.

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Ebene Kurven. Kreisevolvente P{r,(p) bzw. P(x,y) Abwicklung eines gespannten Fadens von einem gegebenen Kreis (Radius a) X — a (cost + tsint) y = a(smt — tcost) Polarkoordinaten: a a cos a yrrr^ (p = t a n oi — cc - tan r - / 1 + / • tan / a Kreisradius t Walzwinkel A. >Tia^ erzeugender Punkt liegt im Abstand c vom Mittelpunkt entfemt (c > a) X = at — csmt y = a — c cos t erzeugender Punkt liegt im Abstand c innerhalb des Rollkreises (c < a) X = at — c sin t y = a — c cos t 2na Epizykloide Epizykloide y Kreis mit Radius b rollt auf der AuBenseite eines Kreises .

Rechtwinkliges Dreieck -b' Satz des Pythagoras Kathetensatz Hohensatz Strahlensatze wenn ABIIA'B', dann gilt a = cp b^ = cq -pq 1. SA:SA' = S B : S B ' SAiAA" =SB:BB^ 2. 7 Geometrische Satze Ubersicht A-17 (Fortsetzung) allgemeine Dreiecke Sinussatz findet Anwendung, wenn eine Seite, der gegeniiberliegende Winkel und eine zweite Seite Oder ein zweiter Winkel gegeben sind Kosinussatz findet Anwendung, wenn drei Seiten bzw. 8 Flachen und Korper Ubersicht A-i8. Inhalt von Flachen. 8 Flachen und Korper Ubersicht A-18 25 (Fortsetzung) Flacheninhalt A Art der Flache Ellipse <=+=^ T = -r/) • d= a-b -n Umfang U « 0,75n{D + d) - 0,5n^Dd -D- Rotation der ebenen Kurve C um die x-Achse ergibt einen (raumlichen) Rotationskorper.

Sinh (x) 1 + tanh 1 - tanh^ (x) = — - y — ; cosh^ (x) 1 - tanh © S) coth^ (x) - 1 = . ^ . smh^ (x) A. 10 Funktionen Ubersicht A-23 (Fortsetzung) Umrechnungen Funktion Funktion sinh (x) cosh (x) sinh (x) - cosh (x) ysinh^ (x) + 1 tanh (x) coth (x) tanh (x) tanh (x) 1 J\ - tanh^ (x) ycoth^(x)-l + ycosh^ (x) - 1 sinh (x) - coth (x) 1 coth (x) yi-tanh^(x) ycoth2(x)-l ysinh^ (x) + 1 ^cosh^ (x) — 1 cosh (x) - 1 coth (x) y/sinh^ (x) + 1 sinh (x) cosh (x) 1 >/cosh^ (x) — 1 tanh (x) - Ubersicht A-24.

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A Bifurcation Analysis of a Differential Equations Model for Mutualism by Gravesa W. G., Peckhamb B., Pastorc J.


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