Cuspidal Envelope Rosettes
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Authors
Rigge, William F., S.J.
Issue Date
1922-01
Type
Article
Language
en_US
Keywords
Rigge Papers , Harmonic Curves
Alternative Title
Abstract
First Paragraph: | A point P moves in the line segment EG, Fig. 1, with simple harmonic motion of p cycles, while this segment makes q revolutions about A with uniform angular speed. Moritz has exhaustively treated the case when the point A is in the line EG or in its prolongation. The writer has shown that when the point A is out of the line EG and the rosette drawn is cuspidal, AL, the distance of EG from A, must be n sin (in which n = p/q) and LR, the distance of R, the mid-point, or point of zero phase, of EG, from its point of tangency L on the tangent circle, must be cos β. The point P remains on an ellipse whose conjugate semi-axis is unity (= ER = RG) and is always parallel to EG, whose major semi-axis = n, and whose center is the sine PR of the phase a distant from A, β being the eccentric angle of P.
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