EquationTrekker


opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the first- or second-order ordinary differential equation eqn for the function x with the independent variable t in the range to .


opens a graphical interface for specifying initial conditions and plotting the resulting numerical solution to the system of two first-order ordinary differential equations eqns for the functions x and y.

EquationTrekker[state]
reopens a graphical interface with the treks saved in the EquationTrekkerState object state.

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  • To use , you first need to load the Equation Trekker Package using Needs["EquationTrekker`"].
  • If eqn is a single first-order ODE, plots of versus t are displayed. If eqn is a single second-order ODE, plots of versus are displayed. If eqns consist of a system of two first-order ODEs, plots of versus are displayed.
  • Treks are invoked by right-clicking a coordinate, which generates a trek that starts at the point specified by the mouse cursor.
  • The initial position of a trek is highlighted in yellow, and by default corresponds to an initial condition specified at t=0. However, only the section of the trek from to is displayed, with the coordinate associated with displayed as a point and the coordinate associated with displayed as an arrowhead.
  • Changing defaults for newly created treks may be accomplished by typing a value in the text field and clicking the _(GraphicsData[CompressedBitmap, eJx1k81rE1EUxU8+Rl10Kbjtxv/CtYrQpeA2FGmL37W7UleCgi4EUXBXLIIo]
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                               xC8wePil) button.
  • generates a modal dialog, and the kernel is controlled by the graphical interface until the window is closed.
  • When the window is closed, a list containing an EquationTrekkerState object and a graphic is returned. The EquationTrekkerState object contains all of the information necessary to reopen the window with the treks that were displayed when the window was closed.
  • The following options can be given:
  • ImageSize{400,400}absolute size of window
    PlotRange{Automatic,{-1,1}}range of values to include
    TrekParameters{}list of parameters and parameter ranges
    TrekGeneratorDifferentialEquationTrekmethod used to generate treks
  • A valid setting for TrekParameters is a list of rules of the form , where range consists of a starting value and a range, . The range specification may also consist of a single value v, which is equivalent to .
  • Valid settings for TrekGenerator are DifferentialEquationTrek and PoincareSection.
  • The default setting TrekGenerator->DifferentialEquationTrek creates treks by following the path of the dependent variables generated using NDSolve.
  • The setting TrekGenerator->PoincareSection creates treks by sampling the phase space. The sampling interval is typically periodic.
  • The setting TrekGenerator->{method,subopts} may be used to include the suboptions subopts for the TrekGenerator method method.

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基本范例  (1)基本范例  (1)

In[1]:=
Click for copyable input

This is a simple example demonstrating how operates:

In[2]:=
Click for copyable input

A window similar to the one below will appear (but with an empty canvas). Click the canvas to add treks: