Editing Helmholtz decomposition (section)

== History ==

The Helmholtz decomposition in three dimensions was first described in 1849<ref name="stokes1849" /> by [[George Gabriel Stokes]] for a theory of [[diffraction]]. [[Hermann von Helmholtz]] published his paper on some [[hydrodynamics|hydrodynamic]] basic equations in 1858,<ref name="helmholtz1858" /><ref name="kustepeli2016" /> which was part of his research on the [[Helmholtz's theorems]] describing the motion of fluid in the vicinity of vortex lines.<ref name="kustepeli2016"/> Their derivation required the vector fields to decay sufficiently fast at infinity. Later, this condition could be relaxed, and the Helmholtz decomposition could be extended to higher dimensions.<ref name="glotzl2023"/><ref name="trancong1993" /><ref name="petrascheck2017"/> For [[Riemannian manifold|Riemannian manifolds]], the Helmholtz-Hodge decomposition using [[differential geometry]] and [[tensor calculus]] was derived.<ref name="glotzl2023" /><ref name="kustepeli2016"/><ref name="sprossig2009"/><ref name="bhatia2013" />

The decomposition has become an important tool for many problems in [[theoretical physics]],<ref name="kustepeli2016" /><ref name="sprossig2009" /> but has also found applications in [[animation]], [[computer vision]] as well as [[robotics]].<ref name="bhatia2013" />