VectorCalculus - Maple Programming Help

Home : Support : Online Help : Mathematics : Vector Calculus : VectorCalculus/GetPVDescription

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

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{pv}≔\mathrm{PositionVector}\left(\left[p\mathrm{cos}\left(p\right),p\mathrm{sin}\left(p\right)\right],{\mathrm{cartesian}}_{x,y}\right)$
 ${\mathrm{pv}}{≔}\left[\begin{array}{c}{p}{}{\mathrm{cos}}{}\left({p}\right)\\ {p}{}{\mathrm{sin}}{}\left({p}\right)\end{array}\right]$ (1)
 > $M≔\mathrm{GetPVDescription}\left(\mathrm{pv},{\mathrm{polar}}_{r,t}\right)$
 ${M}{≔}\left[\sqrt{{{p}}^{{2}}{}{{\mathrm{cos}}{}\left({p}\right)}^{{2}}{+}{{p}}^{{2}}{}{{\mathrm{sin}}{}\left({p}\right)}^{{2}}}{,}{\mathrm{arctan}}{}\left({p}{}{\mathrm{sin}}{}\left({p}\right){,}{p}{}{\mathrm{cos}}{}\left({p}\right)\right)\right]$ (2)
 > $\mathrm{pv2}≔\mathrm{PositionVector}\left(M,{\mathrm{polar}}_{r,t}\right)$
 ${\mathrm{pv2}}{≔}\left[\begin{array}{c}{p}{}{\mathrm{cos}}{}\left({p}\right)\\ {p}{}{\mathrm{sin}}{}\left({p}\right)\end{array}\right]$ (3)
 > $c≔\mathrm{arctan}\left(u\right)$
 ${c}{≔}{\mathrm{arctan}}{}\left({u}\right)$ (4)
 > $\mathrm{pv3}≔\mathrm{PositionVector}\left(\left[\mathrm{cos}\left(u\right)\mathrm{cos}\left(c\right),\mathrm{sin}\left(u\right)\mathrm{cos}\left(c\right),-\mathrm{sin}\left(c\right)\right],{\mathrm{cartesian}}_{x,y,z}\right)$
 ${\mathrm{pv3}}{≔}\left[\begin{array}{c}\frac{{\mathrm{cos}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\\ \frac{{\mathrm{sin}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\\ {-}\frac{{u}}{\sqrt{{{u}}^{{2}}{+}{1}}}\end{array}\right]$ (5)
 > $M≔\mathrm{GetPVDescription}\left(\mathrm{pv3},{\mathrm{spherical}}_{r,p,t}\right)$
 ${M}{≔}\left[\sqrt{\frac{{{\mathrm{cos}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{\mathrm{sin}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{u}}^{{2}}}{{{u}}^{{2}}{+}{1}}}{,}{\mathrm{arctan}}{}\left(\sqrt{\frac{{{\mathrm{cos}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}{+}\frac{{{\mathrm{sin}}{}\left({u}\right)}^{{2}}}{{{u}}^{{2}}{+}{1}}}{,}{-}\frac{{u}}{\sqrt{{{u}}^{{2}}{+}{1}}}\right){,}{\mathrm{arctan}}{}\left(\frac{{\mathrm{sin}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}{,}\frac{{\mathrm{cos}}{}\left({u}\right)}{\sqrt{{{u}}^{{2}}{+}{1}}}\right)\right]$ (6)
 > $\mathrm{simplify}\left(M\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}assuming\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}u::\mathrm{real}$
 $\left[{1}{,}{\mathrm{arctan}}{}\left({1}{,}{-}{u}\right){,}{\mathrm{arctan}}{}\left({\mathrm{sin}}{}\left({u}\right){,}{\mathrm{cos}}{}\left({u}\right)\right)\right]$ (7)