 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.
 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.