FlowLine - Maple Help

Student[VectorCalculus]

 FlowLine
 compute the flow line of a vector field in R^2 or R^3

 Calling Sequence FlowLine(F, G, options)

Parameters

 F - 'Vector'(algebraic); specify the vector field G - 'Vector'(realcons), {list,set}('Vector'(realcons)); specify the starting point(s) of the flow options - (optional) equation(s) of the form option=value where option is one of caption, output, fieldoptions, flowlineoptions, frames.

Description

 • The FlowLine(F, G) calling sequence displays the flow line of the vector field F starting at the point(s) G.
 • The options arguments primarily control plot options.
 • caption = string
 Give the plot a caption.
 – If output = plot, the default caption is Arrows of the vector field, and the flow line(s) emanating from the given initial point(s).
 – If output = animation, the default caption is the one when output = plot plus the sentence During the animation, the marker on the flow line serves to show the direction in which it is traced.
 For more information on typesetting captions, see plot/typesetting.
 output = plot or animation
 This option controls the return value of the command.
 – output = plot returns a plot of the vector field and flow line(s). This is the default value.
 – output = animation returns an animation of an indicator flowing through the vector field (one for each flow line).
 • fieldoptions = list
 A list of plot options for plotting the Vector field. The field is plotted using a call to plots[fieldplot] or plots[fieldplot3d], so options valid for these commands can be passed in this option. For more information on plotting options, see plot/options. The default value is [].
 • flowlineoptions = list
 A list of plot options for plotting the flow line(s). For more information on plotting options, see plot/options. The default value is [].
 • frames = posint
 Specifies the number of frames in the animation. The default value is 16.
 • caption = anything
 A caption for the plot.
 The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right):$

The option scaling=constrained causes both axes to use the same scale, ensuring that a circle appears round.

 > $\mathrm{FlowLine}\left(\mathrm{VectorField}\left(⟨y,-x⟩\right),⟨1,1⟩,\mathrm{scaling}=\mathrm{constrained}\right)$
 > $\mathrm{FlowLine}\left(\mathrm{VectorField}\left(⟨y,-x⟩\right),\left[⟨1,1⟩,⟨2,1⟩\right],\mathrm{scaling}=\mathrm{constrained}\right)$
 > $\mathrm{FlowLine}\left(\mathrm{VectorField}\left(⟨y,-x⟩\right),⟨4,4⟩,\mathrm{flowlineoptions}=\left[\mathrm{thickness}=3,\mathrm{color}=\mathrm{green}\right],\mathrm{fieldoptions}=\left[\mathrm{grid}=\left[8,6\right],\mathrm{color}=\mathrm{magenta}\right],\mathrm{view}=\left[-6..6,-6..6\right],\mathrm{scaling}=\mathrm{constrained}\right)$

The commands to create the plots from the Plotting Guide are

 > $\mathrm{FlowLine}\left(\mathrm{VectorField}\left(⟨y,-x⟩\right),\left\{⟨1,1⟩,⟨-2,1⟩\right\},\mathrm{output}=\mathrm{animation},\mathrm{flowlineoptions}=\left[\mathrm{color}="DarkGreen"\right],\mathrm{scaling}=\mathrm{constrained}\right)$
 > $\mathrm{FlowLine}\left(\mathrm{VectorField}\left(⟨y,-x,z⟩\right),⟨1,1,1⟩,\mathrm{fieldoptions}=\left[\mathrm{transparency}=0.3\right],\mathrm{flowlineoptions}=\left[\mathrm{color}=\mathrm{black},\mathrm{thickness}=4,\mathrm{style}=\mathrm{point}\right],\mathrm{axes}=\mathrm{boxed}\right)$

Compatibility

 • The G parameter was updated in Maple 16.