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VectorCalculus

 GetPVDescription
 return a description of a position Vector in a specified coordinate system.

 Calling Sequence GetPVDescription(pvector) GetPVDescription(pvector, c)

Parameters

 pvector - Vector; the position Vector c - name or name[name, name, ...]; specify the coordinate system, optionally indexed by the coordinate names

Description

 • The GetPVDescription returns a list with the description of pvector in c coordinates.
 • If no coordinate argument is provided, the description of pvector is given with respect to the current coordinate system as long as the dimensions match.
 • The position Vector is always a cartesian Vector rooted at the origin, but its description varies with the choice of coordinates. For more details about position Vectors, see VectorCalculus,Details

Examples

 > with(VectorCalculus):
 > pv := PositionVector([p*cos(p), p*sin(p)], cartesian[x,y]);
 ${\mathrm{pv}}{≔}\left[\begin{array}{c}{p}{}{\mathrm{cos}}{}\left({p}\right)\\ {p}{}{\mathrm{sin}}{}\left({p}\right)\end{array}\right]$ (1)
 > M :=GetPVDescription(pv,polar[r,t]);
 ${M}{≔}\left[\sqrt{{{p}}^{{2}}{}{{\mathrm{cos}}{}\left({p}\right)}^{{2}}{+}{{p}}^{{2}}{}{{\mathrm{sin}}{}\left({p}\right)}^{{2}}}{,}{\mathrm{arctan}}{}\left({p}{}{\mathrm{sin}}{}\left({p}\right){,}{p}{}{\mathrm{cos}}{}\left({p}\right)\right)\right]$ (2)
 > pv2 := PositionVector(M,polar[r,t]);
 ${\mathrm{pv2}}{≔}\left[\begin{array}{c}{p}{}{\mathrm{cos}}{}\left({p}\right)\\ {p}{}{\mathrm{sin}}{}\left({p}\right)\end{array}\right]$ (3)
 > c := arctan(u);
 ${c}{≔}{\mathrm{arctan}}{}\left({u}\right)$ (4)
 > pv3 := PositionVector([cos(u)*cos(c), sin(u)*cos(c), -sin(c)], cartesian[x,y,z]);
 ${\mathrm{pv3}}{≔}\left[\begin{array}{c}\frac{{\mathrm{cos}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\\ \frac{{\mathrm{sin}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\\ {-}\frac{{u}}{\sqrt{{{u}}^{{2}}{+}{1}}}\end{array}\right]$ (5)
 > M := GetPVDescription(pv3, spherical[r,p,t]);
 ${M}{≔}\left[\sqrt{\frac{{{\mathrm{cos}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{\mathrm{sin}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{u}}^{{2}}}{{{u}}^{{2}}{+}{1}}}{,}{\mathrm{arctan}}{}\left(\sqrt{\frac{{{\mathrm{cos}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{\mathrm{sin}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}}{,}{-}\frac{{u}}{\sqrt{{{u}}^{{2}}{+}{1}}}\right){,}{\mathrm{arctan}}{}\left(\frac{{\mathrm{sin}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}{,}\frac{{\mathrm{cos}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\right)\right]$ (6)
 > simplify(M) assuming u::real;
 $\left[{1}{,}{\mathrm{arctan}}{}\left({1}{,}{-}{u}\right){,}{\mathrm{arctan}}{}\left({\mathrm{sin}}{}\left({u}\right){,}{\mathrm{cos}}{}\left({u}\right)\right)\right]$ (7)