Guardat en:
| Autor principal: | |
|---|---|
| Format: | Recurso digital |
| Idioma: | anglès |
| Publicat: |
Zenodo
2025
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.16319505 |
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Taula de continguts:
- <p><span lang="EN-US">This chapter demonstrates how the conserved term </span><span lang="EN-US"> in the spiral exponential function can be naturally derived from the geometric structure of Clifford algebra.</span></p> <p><span lang="EN-US">It begins with examples of divergent and rotational vector fields on the xy-plane and introduces a method for continuously unifying them through the mediating angle θ.</span></p> <p><span lang="EN-US">The structure is then extended to three-dimensional space, describing rotations across the xy, yz, and zx planes using a rotational generator </span></p> <p> </p> <p><span lang="EN-US">By normalizing this generator as </span><span lang="EN-US">, the Clifford exponential function exp(</span><span lang="EN-US">θ) = cosθ + </span><span lang="EN-US">·sinθ is derived.</span></p> <p><span lang="EN-US">For this expansion to hold, </span><span lang="EN-US"> must always span a single plane (a pure blade), which is guaranteed in this construction since the norm of </span><span lang="EN-US"> is always unity.</span></p>