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yes, it is
2. ### Solving system of 2nd order coupled ODEs

Thank you! I did my math by myself and verify your solution, although I searched solution in the form x(t)=x_0e^{i\omega{t}}, so it's just a matter of adding an imaginary unit here and there. It's now clear to me, why one cannot drop fourth derivative - when dealing with rotating reference...
3. ### Solving system of 2nd order coupled ODEs

Context: problem I need to solve is about pendulum in a rotating frame Well, I already dropped all components that are Big O(angle ^3) and beyond in Lagrangian, for the sake of finding analytic solution (otherwise I'd have system of three coupled 2nd order diff equation with variable...
4. ### Solving system of 2nd order coupled ODEs

Well, depends on the problem (I am using small angle approximation as my problem inherently allows me to do that)
5. ### Solving system of 2nd order coupled ODEs

Thanks, worked. But it's strange that equations for x and y have both the same solution (although it shouldn't). I dropped fourth order derivative and solved second order ODE. Case closed for now.
6. ### Solving system of 2nd order coupled ODEs

I have to derive equations of motion from Lagrangian and stumbled upon the following system of equations (constants are simplified, that information is unneeded) \begin{cases} \ddot{x}-A\dot{y}+Bx=0 \\ \ddot{y}+A\dot{x}+Dy=0 \end{cases} This is an extension of a simpler problem where B=D...