# Display a 3D plot of the helical path to emphasize the circular motion

> The animated demo clearly visualizes a helical trajectory, confirming that the object's motion is the superposition of uniform circular motion in the $$x\_1-x\_2$$ plane and constant velocity along the $$x\_3$$ axis. The key mathematical takeaway is the constancy of the object's speed (the magnitude of the velocity vector), which the script calculates as a time-independent value based solely on the fixed parameters $$r\_0, \omega$$, and $$v\_0$$. This constant speed simplifies the calculation of the arc length (total distance traveled), which is found to be directly proportional to the total time elapsed. Visually, the animation emphasizes the uniform radius and the constant pitch of the spiral as the object traces its path.

### :clapper:Narrated Video

{% embed url="<https://youtu.be/J1R051tJz3c>" %}

### :thread:Related Derivation

{% content-ref url="../proof-and-derivation/a-study-of-helical-trajectories-and-vector-dynamics-ht-vd" %}
[a-study-of-helical-trajectories-and-vector-dynamics-ht-vd](https://via-dean.gitbook.io/all/~/revisions/WYsapCOkHSgcDPhymfq8/multifaceted-viewpoint/mathematical-structures-underlying-physical-laws/proof-and-derivation/a-study-of-helical-trajectories-and-vector-dynamics-ht-vd)
{% endcontent-ref %}

### :hammer\_pick:Compound Page

{% embed url="<https://viadean.notion.site/Display-a-3D-plot-of-the-helical-path-to-emphasize-the-circular-motion-HP-CM-2de1ae7b9a3280369289cbfe3ff16fe7?source=copy_link>" %}