Message Boards Message Boards

Full plot of the general solution of an equation

Posted 1 year ago

There are two following equations

\[Sigma] = 
 ArcCos [\[Omega]/(
  Sin [\[Theta] - \[Omega] \[Tau]] \[Epsilon] Sqrt[(1 + \[Alpha]^2)])]


\[CapitalDelta] = 
  2 Cos [\[Theta] - \[Omega] \[Tau]] \[Epsilon] Sqrt[(1 + \[Alpha]^2)]
    Sin[\[Sigma]];

The parameter values are

\[Theta] = \[Pi]/4; \[Tau] = 13.33; \[Epsilon] = 0.021; \[Alpha] = 1; 

I need to plot

\[Omega] \[Tau]  vs   `\[CapitalDelta] \[Tau]`

However as given in the notebook I am not getting the complete plot, it may be because there is a general solution for ArcCos[x], but I cannot understand how to include the general solution here. Kindly suggest.

POSTED BY: Dia Ghosh
3 Replies

Here is a way to get your picture:

x == n /. Solve[y == m, \[Omega]][[1]]
eq = ApplySides[#^2 &, %]
ContourPlot[Evaluate@eq, {x, -1, 1}, {y, -1/2, 1/2}]
POSTED BY: Gianluca Gorni
Posted 1 year ago

What do you mean by "complete plot"? You are explicitly restricting the range with the PlotRange option, so are you saying that the plot is incorrect in that range? Also, I think that for your chosen range for omega, you will have non-real values for n, so are you asking how to plot complex values?

POSTED BY: Eric Rimbey
Posted 1 year ago

The figure is given below, I want to plot the first one

enter image description here

Please suggest, how do I include the general solution of ArcCos [x]? I have considered sigma = ArcCos[x], however it may have other solutions at 2n pi+/- ArcCos[x].

POSTED BY: Dia Ghosh
Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract