running in parallel · 2 dots · 1 gyro · 3 axes + 3 shadows

The Triad & Its Shadow

a visualization — the triad & the shadows are real geometry; pinning the dots is a staging choice
One gyro, shown as its three rotational axes — an axle and two wheel diameters — precessing about the vertical. A floor below catches their three shadows. And two dots: the real one at the pivot 0,0,0, and its shadow on the floor directly beneath. Real frame above, projection below.
floor — the shadow plane (one dimension dropped)
axle / spin axis wheel axis 1 wheel axis 2 dot at pivot (0,0,0) shadow dot
spin

Two dots — pivot & projection

The filled dot is the ephemeral dot at the 3D pivot, 0,0,0 — the still point the whole gyro turns around.

The hollow dot is its shadow: the same point projected straight down onto the floor. The dashed line is the drop. Two dots, one real and one cast — and this shadow is honest geometry, a projection, not the muddled "photon-shadow" from before.

3 axes vs 3 shadow axes

The three bright axes are a real orthonormal frame — the rotational axes of a 3-axis gyro (axle + two wheel diameters).

Their shadows are the same three axes projected onto the floor — 3D flattened to 2D, one dimension dropped. Watch the lengths: an axis tipping toward vertical casts a short shadow, one lying flat casts a long one. Shadow length reads out tilt.

Honest footing. The precessing triad and its orthographic shadows are real geometry, drawn to scale. What's a staging choice is where the dots sit — the pivot and its projection — chosen because they're the natural still-point and its shadow, not because the dot has physics of its own. As always: the ephemeral dot only does what it's placed to do — mark the center while the frame turns, and cast one honest shadow.