Document JFM 25.1079.03

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Sur la détermination des trajectoires orthogonales de quelques familles de courbes planes dont l’équation est donnée en coordonnées bipolaires. (French) JFM 25.1079.03

Nouv. Ann. XIII. 283-292 (1894).

Von der Curvenschar \(f(r, r')=h\) und ihrer Differentialgleichung \(\frac{\partial f}{\partial r}dr + \frac{\partial f}{\partial r'}dr'=0\) gelangt man zu den orthogonalen Curven, wenn \(dr/dr'\) ersetzt wird durch \(rd\theta/r'd\theta'\), wobei \(\theta\) und \(\theta'\) die zugehörigen biangulären Coordinaten sind; in manchen Fällen kann man \(r\), \(r'\) eliminiren und dann integriren.

Reviewer: Müller, R. (Berlin)

JFM Section:

Neunter Abschnitt. Analytische Geometrie. Capitel 2. Analytische Geometrie der Ebene. A. Allgemeine Theorie der ebenen Curven.

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