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VectorCalculus[GetPVDescription] - return a description of a position Vector in a specified coordinate system.
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Calling Sequence
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GetPVDescription(pvector)
GetPVDescription(pvector, c)
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Parameters
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pvector
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Vector; the position Vector
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c
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name or name[name, name, ...]; specify the coordinate system, optionally indexed by the coordinate names
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Description
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The GetPVDescription returns a list with the description of pvector in c coordinates.
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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.
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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
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Examples
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>
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![pv := PositionVector([p*cos(p), p*sin(p)], cartesian[x, y])](/support/helpjp/helpview.aspx?si=4984/file03378/math82.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4984/file03378/math85.png)
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![M := GetPVDescription(pv, polar[r, t])](/support/helpjp/helpview.aspx?si=4984/file03378/math89.png)
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![M := [(p^2*cos(p)^2+p^2*sin(p)^2)^(1/2), arctan(p*sin(p), p*cos(p))]](/support/helpjp/helpview.aspx?si=4984/file03378/math92.png)
| (2) |
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![pv2 := PositionVector(M, polar[r, t])](/support/helpjp/helpview.aspx?si=4984/file03378/math96.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4984/file03378/math99.png)
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| (4) |
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![pv3 := PositionVector([cos(u)*cos(c), sin(u)*cos(c), -sin(c)], cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4984/file03378/math110.png)
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/(1+u^2)^(1/2)], [sin(u)/(1+u^2)^(1/2)], [-u/(1+u^2)^(1/2)]])](/support/helpjp/helpview.aspx?si=4984/file03378/math113.png)
| (5) |
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![M := GetPVDescription(pv3, spherical[r, p, t])](/support/helpjp/helpview.aspx?si=4984/file03378/math117.png)
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![M := [(cos(u)^2/(1+u^2)+sin(u)^2/(1+u^2)+u^2/(1+u^2))^(1/2), arctan((cos(u)^2/(1+u^2)+sin(u)^2/(1+u^2))^(1/2), -u/(1+u^2)^(1/2)), arctan(sin(u)/(1+u^2)^(1/2), cos(u)/(1+u^2)^(1/2))]](/support/helpjp/helpview.aspx?si=4984/file03378/math120.png)
| (6) |
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![`assuming`([simplify(M)], [u::real])](/support/helpjp/helpview.aspx?si=4984/file03378/math124.png)
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![[1, arctan(1, -u), arctan(sin(u), cos(u))]](/support/helpjp/helpview.aspx?si=4984/file03378/math127.png)
| (7) |
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