VectorFieldPlots`
VectorFieldPlots`

# HamiltonianFieldPlot

As of Version 7.0, HamiltonianFieldPlot has been superseded by VectorPlot.

HamiltonianFieldPlot[f,{x,xmin,xmax},{y,ymin,ymax}]

generates a plot of the Hamiltonian vector field of the scalar-valued function f as a function of x and y.

HamiltonianFieldPlot[f,{x,xmin,xmax,dx},{y,ymin,ymax,dy}]

uses steps dx in variable x, and steps dy in variable y.

# Details and Options

• To use HamiltonianFieldPlot, you first need to load the Vector Field Plotting Package using Needs["VectorFieldPlots`"].
• The derivatives of f are calculated analytically.
• HamiltonianFieldPlot has the same options as Graphics, with the following additions and changes:
•  ColorFunction None a function to use for coloring the vectors by their magnitude MaxArrowLength None length of the largest vector to be drawn, applied after the ScaleFunction, but before the ScaleFactor PlotPoints 15 the number of evaluation points in each direction ScaleFactor Automatic linearly rescales the vectors so the longest vector is equal to this value; Automatic fits the vectors in the mesh, None eliminates the rescaling ScaleFunction None a function to use for rescaling the magnitude of vectors

# Examples

## Basic Examples(1)

Hamiltonian vector field of as and run from 0 to :

Wolfram Research (2008), HamiltonianFieldPlot, Wolfram Language function, https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html.

#### Text

Wolfram Research (2008), HamiltonianFieldPlot, Wolfram Language function, https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html.

#### CMS

Wolfram Language. 2008. "HamiltonianFieldPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html.

#### APA

Wolfram Language. (2008). HamiltonianFieldPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html

#### BibTeX

@misc{reference.wolfram_2024_hamiltonianfieldplot, author="Wolfram Research", title="{HamiltonianFieldPlot}", year="2008", howpublished="\url{https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html}", note=[Accessed: 25-April-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_hamiltonianfieldplot, organization={Wolfram Research}, title={HamiltonianFieldPlot}, year={2008}, url={https://reference.wolfram.com/language/VectorFieldPlots/ref/HamiltonianFieldPlot.html}, note=[Accessed: 25-April-2024 ]}