The changecoords(expr, vars, coord, new_vars) calling sequence changes the expression expr in cartesian coordinates vars to an expression in the new coordinate system coord. The new expression is written in terms of the original variables. An optional fourth argument new_vars can be used to specify the set of variables for the new coordinate system.

The argument coord must be from the set of accepted coordinate types.

In three dimensions:

In two dimensions:

The conversions from the coordinate systems to cartesian coordinates are listed in the help page for coords.

There are two widely used conventions for how to represent spherical coordinates. When you use the coordinate system name spherical, Maple uses one of those conventions depending on whether you are using the Physics (and VectorCalculus) package or not.  You can specify which definition is used by providing either the coordinate system name spherical_math or spherical_physics. For more information, see coords.

New coordinate systems can be introduced by using the addcoords routine. Once introduced, they are recognized by the changecoords command.

See also the plots[changecoords] command.  Note that issuing with(plots) rebinds the name changecoords, so :-changecoords must be used to run this command.

$\mathrm{changecoords}\left(x^2+y^2\,\left[x\,y\right]\,\mathrm{polar}\right)$

$x^2{\cos \left(y\right)}^2+x^2{\sin \left(y\right)}^2$

$\mathrm{changecoords}\left(x^2+y^2\,\left[x\,y\right]\,\mathrm{polar}\,\left[r\,\mathrm{\theta }\right]\right)$

$r^2{\cos \left(\mathrm{\theta }\right)}^2+r^2{\sin \left(\mathrm{\theta }\right)}^2$

$\mathrm{changecoords}\left(x-y\,\left[x\,y\right]\,\mathrm{logarithmic}\right)$

$\frac{\ln \left(x^2+y^2\right)-2\arctan \left(\frac{y}{x}\right)}{\mathrm{\pi }}$

$\mathrm{changecoords}\left(xyz\,\left[x\,y\,z\right]\,\mathrm{bipolarcylindrical}\right)$

$\frac{\sinh \left(y\right)\sin \left(x\right)z}{{\left(\cosh \left(y\right)-\cos \left(x\right)\right)}^2}$

$\mathrm{changecoords}\left(xy+xz-y\,\left[x\,y\,z\right]\,\mathrm{tangentcylindrical}\,\left[u\,v\,w\right]\right)$

$\frac{u^{3}w+u{v}^{2}w-u^{2}v-v^3+uv}{{\left(u^2+v^2\right)}^2}$

$\mathrm{changecoords}\left(xyz\,\left[x\,y\,z\right]\,\mathrm{spherical}\,\left[r\,\mathrm{\theta }\,\mathrm{\phi }\right]\right)$

$r^3\cos \left(\mathrm{\theta }\right){\sin \left(\mathrm{\phi }\right)}^2\sin \left(\mathrm{\theta }\right)\cos \left(\mathrm{\phi }\right)$