How can I obtain the derivative of a vector?

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student 2015-2-17

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评论： Star Strider 2015-2-18

Hi, I have solved a system of ODEs with the solver ODE45 , obtaining the vector T and Y, which is a matrix of Nx6; N time points (length of vector of time points T) and 6 vectors, x1,x2,x3,dx1,dx2,dx3, displacements and velocities of three masses. I would like to obtain the vector of accelerations of x1,x2,x3. Could somebody please help me? Thank you very much!

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Star Strider 2015-2-17

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Plug your ‘t’ vector and ‘y’ values matrix back into your ODE function. It will give you all the derivatives because that’s what you wrote it to provide.

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student 2015-2-18

Hi Roger,

thank you for your answer. How can I plug the vectors into my function to obtain the answer? Sorry, but I´m new in Matlab...

Star Strider 2015-2-18

在 MATLAB Online 中打开

I don’t know if you’re addressing me or Roger. Assuming me, because you’re Commenting on my Answer, you just plug the integrated values of ‘t’ and ‘y’ (returned by ode45) into your ODE function. So if ‘odefun’ is the name of your ODE function and it is written as:

function dy = odefun(t,y)

to get the derivative matrix, simply call it as:

dy = odefun(t,y);

where ‘t’ is the vector of times that ode45 returns, and ‘y’ is the matrix of solutions ode45 returns. The ‘dy’ matrix is the matrix of derivatives you want, at times corresponding to ‘t’.

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Roger Stafford 2015-2-17

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在 MATLAB Online 中打开

You can get an approximation to the derivative of dx1, dx2, and dx3 using matlab's 'gradient' function. If you would prefer a higher order approximation, you can find the code I wrote for a parabolic approximations at:

http://www.mathworks.com/matlabcentral/answers/175172

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student 2015-2-18

thank you!

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Torsten 2015-2-18

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I guess you defined the ODEs as acceleration = f(displacement,velocity). So just repeat the calculations of acceleration (y'') for the solution variables you got from ODE45.

Best wishes

Torsten.