- #1
sampahmel
- 21
- 0
Dear all,
Draw behavior around (0,0) of solutions to the following nonlinear system
[tex]
\left(
\begin{array}{c}
x'(t) \\
y'(t)
\end{array}\right) =\left(
\begin{array}{cc}
cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\
-x(t) + {y(t)}^2 + y(t) + sin {y(t)}
\end{array}\right)\left(
[/tex]
My questions are:
1.) If (0,0) is not specified, do we automatically take (0,0) and draw behavior around it? If no, which point should be chosen?
For the next two questions, I know the rules for this forum are that I have to show my work, but I really don't have anything. All I can tell you is typically I just convert the LHSs of equations into matrix product. But here, because there is trigonometric functions of x(t) & y(t) and also squares of them, I feel matrix cannot help me in this case.
2.) How do you deal with the fact that x(t) and y(t) have cos & sin before it (ie. cos {x(t)} + sin {x(t)} ), instead of cos (t) * x(t)?
3.) How do you deal with the squares of x(t) & the third power of y(t) when converting it into a matrix product?
If you can't show them, at least tell me the name of the method to deal with these problems so I can google them up. But preferably, at least show me how you convert them into matrix form, please.
Thank you.
Homework Statement
Draw behavior around (0,0) of solutions to the following nonlinear system
[tex]
\left(
\begin{array}{c}
x'(t) \\
y'(t)
\end{array}\right) =\left(
\begin{array}{cc}
cos {x(t)} + sin {x(t)} + {x(t)}^2 + {x(t)}^2{y(t)}^3 \\
-x(t) + {y(t)}^2 + y(t) + sin {y(t)}
\end{array}\right)\left(
[/tex]
Homework Equations
My questions are:
1.) If (0,0) is not specified, do we automatically take (0,0) and draw behavior around it? If no, which point should be chosen?
For the next two questions, I know the rules for this forum are that I have to show my work, but I really don't have anything. All I can tell you is typically I just convert the LHSs of equations into matrix product. But here, because there is trigonometric functions of x(t) & y(t) and also squares of them, I feel matrix cannot help me in this case.
2.) How do you deal with the fact that x(t) and y(t) have cos & sin before it (ie. cos {x(t)} + sin {x(t)} ), instead of cos (t) * x(t)?
3.) How do you deal with the squares of x(t) & the third power of y(t) when converting it into a matrix product?
If you can't show them, at least tell me the name of the method to deal with these problems so I can google them up. But preferably, at least show me how you convert them into matrix form, please.
Thank you.
The Attempt at a Solution
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