MATLAB: Simplification of an algebraic equation

algebraic equation

This equation is output of a matlab program.please suggest method To get simplified equation form i.e,simple co efficents for different order.
q0 - 0.00784*q1*(94.1*q0^2 + 368.0*q1^2 + 149.0*q2^2) + 0.00344*q1*(1511.0*q0^2 + 5900.0*q1^2 + 2400.0*q2^2) + 0.0902*q0*(106.0*q0^2 + 175.0*q1^2 + 74.7*q2^2) - 1.45*10^(-4)*q2*(- 2044.0*q0^2 + 2199.0*q1^2 + 711.0*q2^2) - 0.103*q0*(2488.0*q0^2 + 2011.0*q1^2 + 934.0*q2^2) + 3.2*10^(-4)*q2*(2488.0*q0^2 + 2011.0*q1^2 + 934.0*q2^2)

Best Answer

syms q0 q1 q2 
e=q0 - 0.00784*q1*(94.1*q0^2 + 368.0*q1^2 + 149.0*q2^2) + 0.00344*q1*(1511.0*q0^2 + 5900.0*q1^2 + 2400.0*q2^2) + 0.0902*q0*(106.0*q0^2 + 175.0*q1^2 + 74.7*q2^2) - 1.45*10^(-4)*q2*(- 2044.0*q0^2 + 2199.0*q1^2 + 711.0*q2^2) - 0.103*q0*(2488.0*q0^2 + 2011.0*q1^2 + 934.0*q2^2) + 3.2*10^(-4)*q2*(2488.0*q0^2 + 2011.0*q1^2 + 934.0*q2^2)
a=simplify(e)

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MATLAB: Solving System of 4 Non-Linear Equations

fsolve is a numerical solver - use vpasolve instead:

syms A B C t0
eq1 = A*sin(2*B*pi*0.2 + 2*B*pi*(0 - t0)^2)+C - sin(2*pi*0.2); 
eq2 = A*sin(2*B*pi*0.4 + 2*B*pi*(0 - t0)^2)+C - sin(2*pi*0.4);
eq3 = A*sin(2*B*pi*0.5 + 2*B*pi*(0 - t0)^2)+C - sin(2*pi*0.5);
eq4 = A*sin(2*B*pi*0.7 + 2*B*pi*(-t0)^2)+C - sin(2*pi*0.7);
result = vpasolve([eq1,eq2,eq3,eq4]);
A = result.A
B = result.B
C = result.C
t0 = result.t0

I allowed myself to replace 3.1416 by pi

MATLAB: How to resample points with preset angle

Try this

x = points(:,1); % first column of points you shared
y = points(:,2);  % second column of points
x_new = interp1(linspace(0, 2*pi, numel(x)), x, 0:2*pi/37:2*pi);
y_new = interp1(linspace(0, 2*pi, numel(y)), y, 0:2*pi/37:2*pi);

x_new and y_new contains the required points.

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Related Solutions

MATLAB: Solving System of 4 Non-Linear Equations

MATLAB: How to resample points with preset angle

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