I have some coupled nonlinear ordinary differential equations. Three equations have three 2nd order derivative coupled together. Can someone tell me how I can get the response
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I have some coupled nonlinear ordinary differential equations. Three equations have three 2nd order derivative coupled together. Can someone tell me how I can get the response, numerically? i.e t vs x , t vs theta dot plots.
Thanks in advance
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James Tursa
2022-9-21
编辑:James Tursa
2022-9-21
Another related approach is to isolate all the 2nd derivatives on the LHS and put everything else on the RHS. Then pick off the coefficients of the 2nd order derivatives to form a matrix problem that you solve for the 2nd derivatives. E.g., the matrix problem would look something like this based on your comment edits:
A*z = b
where
A = [ 1 0 -f*sin(theta);
0 1 f*sin(theta);
-m*e*sin(theta) m*e*cos(theta) (m*e^2+Ip)/B^2]
and
z = [x_dotdot; y_dotdot; theta_dotdot]
and
b = 3x1 vector with all the other stuff from RHS
Then solve for z to get the 2nd derivatives.
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