Definition:Trochoid/Prolate
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Definition
Consider a circle $C$ rolling without slipping along a straight line.
Consider a point $P$ on the line of a radius of $C$ at a distance $b$ from the center of $C$.
Let $b > a$.
The curve traced out by $P$ is called a prolate trochoid.
Graph
Also known as
A prolate trochoid can also be seen referred to as an extended cycloid.
According to Ephraim J. Borowski and Jonathan M. Borwein in their Dictionary of Mathematics of $1989$, the literature is inconsistent as to whether the term prolate or curtate is used to denote this object.
$\mathsf{Pr} \infty \mathsf{fWiki}$'s usage of these terms will be consistent.
Also see
- Results about prolate trochoids can be found here.
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 11$: Special Plane Curves: Trochoid: $11.20$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): cycloid
- 2009: Murray R. Spiegel, Seymour Lipschutz and John Liu: Mathematical Handbook of Formulas and Tables (3rd ed.) ... (previous) ... (next): $\S 9$: Special Plane Curves: Trochoid: $9.20.$