Definition:Trochoid
Jump to navigation
Jump to search
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 $C$.
The curve traced out by $P$ is called a trochoid.
Curtate
Let $b < a$.
The curve traced out by $P$ is called a curtate trochoid.
Graph
Prolate
Let $b > a$.
The curve traced out by $P$ is called a prolate trochoid.
Graph
Cycloid
The special case where $a = b$ is usually treated separately:
Consider a circle rolling without slipping along a straight line.
Consider a point $P$ on the circumference of this circle.
The curve traced out by $P$ is called a cycloid.
Graph
Also see
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