changecoords - Maple Help

changecoords

change expression in cartesian coordinates to a new coordinate system

 Calling Sequence changecoords(expr, vars, coord, new_vars)

Parameters

 expr - expression vars - list of 2 or 3 variables coord - name; new coordinate system new_vars - (optional) list of 2 or 3 variables

Description

 • 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:

 bipolarcylindrical bispherical cardioidal cardioidcylindrical casscylindrical confocalellip confocalparab conical cylindrical ellcylindrical ellipsoidal hypercylindrical invcasscylindrical invellcylindrical invoblspheroidal invprospheroidal logcoshcylindrical logcylindrical maxwellcylindrical oblatespheroidal paraboloidal paraboloidal2 paracylindrical prolatespheroidal rosecylindrical sixsphere spherical tangentcylindrical tangentsphere toroidal

 In two dimensions:

 bipolar cardioid cassinian elliptic hyperbolic invcassinian invelliptic logarithmic logcosh maxwell parabolic polar rose tangent

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

Examples

 > $\mathrm{changecoords}\left({x}^{2}+{y}^{2},\left[x,y\right],\mathrm{polar}\right)$
 ${{x}}^{{2}}{}{{\mathrm{cos}}{}\left({y}\right)}^{{2}}{+}{{x}}^{{2}}{}{{\mathrm{sin}}{}\left({y}\right)}^{{2}}$ (1)
 > $\mathrm{changecoords}\left({x}^{2}+{y}^{2},\left[x,y\right],\mathrm{polar},\left[r,\mathrm{\theta }\right]\right)$
 ${{r}}^{{2}}{}{{\mathrm{cos}}{}\left({\mathrm{\theta }}\right)}^{{2}}{+}{{r}}^{{2}}{}{{\mathrm{sin}}{}\left({\mathrm{\theta }}\right)}^{{2}}$ (2)
 > $\mathrm{changecoords}\left(x-y,\left[x,y\right],\mathrm{logarithmic}\right)$
 $\frac{{\mathrm{ln}}{}\left({{x}}^{{2}}{+}{{y}}^{{2}}\right){-}{2}{}{\mathrm{arctan}}{}\left(\frac{{y}}{{x}}\right)}{{\mathrm{\pi }}}$ (3)
 > $\mathrm{changecoords}\left(xyz,\left[x,y,z\right],\mathrm{bipolarcylindrical}\right)$
 $\frac{{\mathrm{sinh}}{}\left({y}\right){}{\mathrm{sin}}{}\left({x}\right){}{z}}{{\left({\mathrm{cosh}}{}\left({y}\right){-}{\mathrm{cos}}{}\left({x}\right)\right)}^{{2}}}$ (4)
 > $\mathrm{changecoords}\left(xy+xz-y,\left[x,y,z\right],\mathrm{tangentcylindrical},\left[u,v,w\right]\right)$
 $\frac{{{u}}^{{3}}{}{w}{+}{u}{}{{v}}^{{2}}{}{w}{-}{{u}}^{{2}}{}{v}{-}{{v}}^{{3}}{+}{u}{}{v}}{{\left({{u}}^{{2}}{+}{{v}}^{{2}}\right)}^{{2}}}$ (5)
 > $\mathrm{changecoords}\left(xyz,\left[x,y,z\right],\mathrm{spherical},\left[r,\mathrm{\theta },\mathrm{\phi }\right]\right)$
 ${{r}}^{{3}}{}{{\mathrm{sin}}{}\left({\mathrm{\phi }}\right)}^{{2}}{}{\mathrm{cos}}{}\left({\mathrm{\theta }}\right){}{\mathrm{sin}}{}\left({\mathrm{\theta }}\right){}{\mathrm{cos}}{}\left({\mathrm{\phi }}\right)$ (6)