# use a simple Euler numerical integration method to simulate the precession over time

> The demo vividly illustrates the principle of pure precession, where the angular momentum vector $$L$$ rotates steadily around the fixed axis $$v$$. The underlying mechanism is the cross-product nature of the differential equation, $$\frac{d L}{d t}=v \times L$$, which ensures that the change in $$L$$ is perpetually perpendicular to $$L$$ itself; this guarantees that the magnitude of $$L$$ is conserved. The resulting motion is the tracing of a cone around $$v$$, with the rate of precession $$\Omega$$ being constant and equal to $$|v|$$. The simulation confirms that regardless of the initial conditions, the magnitude of $$L$$ and its inner product with $$v$$ are held constant throughout the rotation, precisely matching the theoretical proof.

### :clapper:Narrated Video

{% embed url="<https://youtu.be/h6IsSgg0dBg>" %}

### :thread:Related Derivation

{% content-ref url="../proof-and-derivation/the-power-of-cross-products-a-visual-guide-to-precessing-vectors-cp-pv" %}
[the-power-of-cross-products-a-visual-guide-to-precessing-vectors-cp-pv](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/proof-and-derivation/the-power-of-cross-products-a-visual-guide-to-precessing-vectors-cp-pv)
{% endcontent-ref %}

### :hammer\_pick:Compound Page

{% content-ref url="use-a-simple-euler-numerical-integration-method-to-simulate-the-precession-over-time" %}
[use-a-simple-euler-numerical-integration-method-to-simulate-the-precession-over-time](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/animated-results/use-a-simple-euler-numerical-integration-method-to-simulate-the-precession-over-time)
{% endcontent-ref %}