🧄The Power of Cross Products: A Visual Guide to Precessing Vectors

The precession of a vector is a direct consequence of a cross product in its differential equation, which ensures that the vector's magnitude and its angle relative to the precession axis remain constant. This stability arises because the change in the vector ( $d L / d t$ ) is always perpendicular to the vector itself and the constant vector it's precessing around.

🎬 a 3D simulation of vector precession

the precession of a vector is a direct consequence of a cross product in its differential equation. The simulation visually demonstrates how the change in $L$ (i.e., $d L / d t$) is always perpendicular to both $v$ and $L$. Because the change is always perpendicular to $L$ itself, the length of $L$ doesn't change, only its direction. The interactive sliders let you set the initial conditions, making it clear that while the specific magnitude and inner product of $L$ depend on its starting state, those values are then held constant throughout the precession, precisely as the mathematical proof predicts.

🧄Mathematical Proof

The Power of Cross Products: A Visual Guide to Precessing Vectors | Proof and Derivationviadean on Notion