ChangeCoordinates changes the coordinates of a given expression, possible a vector function, to the indicated system of coordinates. Optionally, when the argument alsothebasis is given, the unit vectors present in A are also rewritten in terms of the unit vectors associated to the system of coordinates indicated. ChangeCoordinates is thus complementary to ChangeBasis. For the conventions used in the Physics[Vectors] subpackage to represent vector functions, see conventions.

The coordinates are changed according to the following. From cartesian $\left[x\,y\,z\right]$ to cylindrical $\left[\mathrm{\rho }\,\mathrm{\phi }\,z\right]$:

From cartesian $\left[x\,y\,z\right]$ to spherical $\left[r\,\mathrm{\theta }\,\mathrm{\phi }\right]$ (note the ordering of the angles):

For the formulas used to change the unit vectors when alsothebasis is passed, see ChangeBasis.

The %ChangeCoordinates is the inert form of ChangeCoordinates, that is: it represents the same mathematical operation while holding the operation unperformed. To activate the operation use value.

$\mathrm{with}\left(\mathrm{Physics}\left[\mathrm{Vectors}\right]\right)$

$\left[\mathrm{\&x}\,\mathrm{`+`}\,\mathrm{`.`}\,\mathrm{Assume}\,\mathrm{ChangeBasis}\,\mathrm{ChangeCoordinates}\,\mathrm{CompactDisplay}\,\mathrm{Component}\,\mathrm{Curl}\,\mathrm{DirectionalDiff}\,\mathrm{Divergence}\,\mathrm{Gradient}\,\mathrm{Identify}\,\mathrm{Laplacian}\,\nabla \,\mathrm{Norm}\,\mathrm{ParametrizeCurve}\,\mathrm{ParametrizeSurface}\,\mathrm{ParametrizeVolume}\,\mathrm{Setup}\,\mathrm{Simplify}\,\mathrm{`^`}\,\mathrm{diff}\,\mathrm{int}\right]$

$\mathrm{Setup}\left(\mathrm{mathematicalnotation}=\mathrm{true}\right)$

$\left[\mathrm{mathematicalnotation}=\mathrm{true}\right]$

$R≔x\mathrm{\_i}+y\mathrm{\_j}+z\mathrm{\_k}$

$R≔x\stackrel{\wedge }{i}+y\stackrel{\wedge }{j}+z\stackrel{\wedge }{k}$

$\mathrm{ChangeCoordinates}\left(R\,2\right)$

$\stackrel{\wedge }{i}\mathrm{\rho }\cos \left(\mathrm{\phi }\right)+\stackrel{\wedge }{j}\mathrm{\rho }\sin \left(\mathrm{\phi }\right)+z\stackrel{\wedge }{k}$

$\mathrm{ChangeCoordinates}\left(R\,\mathrm{spherical}\right)$

$r\sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\phi }\right)\stackrel{\wedge }{i}+r\sin \left(\mathrm{\theta }\right)\sin \left(\mathrm{\phi }\right)\stackrel{\wedge }{j}+r\stackrel{\wedge }{k}\cos \left(\mathrm{\theta }\right)$

$\mathrm{ChangeCoordinates}\left(R\,\mathrm{cylindrical}\,\mathrm{alsothebasis}\right)$

$z\stackrel{\wedge }{k}+\mathrm{\rho }\stackrel{\wedge }{\mathrm{\rho }}$

$\mathrm{ChangeCoordinates}\left(R\,3\,\mathrm{alsothebasis}\right)$

$r\stackrel{\wedge }{r}$