"James Waldby" wrote in message news:uf8c26$nkgc$
1@dont-email.me...
Jim Wilkins <
muratlanne@gmail.com> wrote:
...
The sine function is a one-dimensional representation of rotation at
constant speed, such as the height of a bicycle tire valve when the wheel
is
coasting, neither gaining nor losing speed or energy. Thus it's the AC equivalent of a steady state. The cosine is the same, at a right angle to
the sine, and the two together define and can recreate a circle, and as electrical waveforms they can transmit and fully reconstruct rotary motion theoretically without loss.
...
On a constant-forward-speed bicycle, tire valves follow cycloidal
paths. See first picture,
https://en.wikipedia.org/wiki/Cycloid .
For sine or cosine the wheel would need to be rotating in place.
----------------------
That's true if your frame of reference is standing on the street. If it's riding or repairing the bicycle my frame of reference applies. Since sine
and cosine are tied together usually only the sine is used to adequately describe the waveform.
In digital radio the sine is the in-phase real component and the cosine the imaginary quadrature component of a complex number, imaginary meaning the dimension where the square root of -1 exists. Complex number math is a
perfect fit for this and allows an equation to contain both without them interacting unless desired, such as to find the resultant angle. Here's a non-mathematical description:
https://www.techtarget.com/searchnetworking/definition/QAM
The same analysis applies to brushless motors where the rotating magnetic
field can be synthesized electronically from battery DC.
--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)