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Math Help - Linearizing ordinary differential equations

  1. #1
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    Linearizing ordinary differential equations

    Hi guys, im trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I cant get a proper reference on this state-space model.

    Attached is the non-linear ode, the partial derivative of the non-linear ode and the state-space model of jacobian matrix.

    Can someone enhance or explain how they got the state-space model as the transformation, is it a fix formulation. Sorry for asking this way cause I cant find any books or reference referring or explaining this. Please help me! thanks!
    Attached Thumbnails Attached Thumbnails Linearizing ordinary differential equations-jacobian-1.jpg   Linearizing ordinary differential equations-jacobian-2.jpg  
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