I am trying to visualise 3D loci.
Example: a person is on the London Eye (a type of ferris wheel with a large capsule, see here: The London Eye's official website for the best online ticket prices, guaranteed.). She paces up and down in the capsule as it goes round. What would the path traced out by her look like in 2D and 3D? I am pretty sure I have it in 2D -a straight line the length of the capsule on a circle and repeated periodically over the circumference of the circle, but not sure about 3D.
A person is on the London Eye (a Ferris wheel with a large capsule).
She paces up and down in the capsule as it goes round.
You mean back-and-forth or end-to-end, don't you?
What would the path traced out by her look like in 2D and 3D?
I will assume that the pacing is done in simple harmonic motion.
Suppose a lap is a walk from one end of the capsule to the other and back.
Suppose further that she walks 30 laps during one revolution of the wheel.
Get a huge strip of paper.
Its length is the circumference of the wheel.
Its width is the length of the capsule.
On the strip, fit thirty cycles of a sine curve.
Tape together the ends of the strip, forming a wheel.
The sine graph is the path taken by the person.