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VectorCalculus[ConvertVector] - converts Cartesian free Vectors, rooted Vectors and position Vectors among themselves
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Calling Sequence
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ConvertVector(v,form)
ConvertVector(v,form, root )
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Parameters
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v
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'Vector'(algebraic); the Cartesian free Vector, rooted Vector or position Vector to convert
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form
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name; specify the type of Vector to be converted to: free, rooted or position
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root
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(optional) list(algebraic) or Vector(algebraic); root point of the converted Vector
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Description
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The ConvertVector command converts Cartesian free Vectors, rooted Vectors and position Vectors among themselves by specifying the desired type. If v is not a Cartesian Vector an error is raised.
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If form is rooted, the root point can be specified as a list or a free Vector with the extra optional parameter root. If root is a list, it is interpreted in Cartesian coordinates, if it is a free Vector in non-Cartesian coordinates, an appropiate transformation is made to obtain a Cartesian root.
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If form is rooted, v is a free, rooted or position Vector and root is provided, the result is the Vector rooted at root.
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If form is rooted, v is a position Vector and root is not provided, then the Vector is rooted at the Cartesian origin.
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If form is rooted, v is a free Vector and root is not provided an error is raised.
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Examples
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![ConvertVector(PositionVector([1, p], parabolic), 'rooted')](/support/helpjp/helpview.aspx?si=4982/file03365/math134.png)
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*p^2], [p]])](/support/helpjp/helpview.aspx?si=4982/file03365/math137.png)
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![pv := PositionVector([p*cos(p), p*sin(p)], cartesian[x, y])](/support/helpjp/helpview.aspx?si=4982/file03365/math141.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4982/file03365/math144.png)
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], [p*sin(p)]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4982/file03365/math151.png)
| (3) |
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4982/file03365/math158.png)
| (4) |
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![Matrix([[`Type: `, `Rooted Vector`], [`Components: `, [p*cos(p), p*sin(p)]], [`Coordinates: `, cartesian[x, y]], [`Root Point: `, [0, 0]]])](/support/helpjp/helpview.aspx?si=4982/file03365/math165.png)
| (5) |
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![Vector[column]([[0], [0]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4982/file03365/math172.png)
| (6) |
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![v3 := ConvertVector(pv, 'rooted', [1, 1])](/support/helpjp/helpview.aspx?si=4982/file03365/math176.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4982/file03365/math179.png)
| (7) |
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![Vector[column]([[1], [1]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4982/file03365/math186.png)
| (8) |
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![v4 := ConvertVector(pv, 'rooted', Vector(`<,>`(1, (1/2)*Pi), coords = polar[u, v]))](/support/helpjp/helpview.aspx?si=4982/file03365/math190.png)
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], [p*sin(p)]])](/support/helpjp/helpview.aspx?si=4982/file03365/math193.png)
| (9) |
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![Vector[column]([[0], [1]], ["x", "y"])](/support/helpjp/helpview.aspx?si=4982/file03365/math200.png)
| (10) |
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