Tutorial: Systems of Nonlinear Equation

For n equations with n unknowns

Problem 1

Solve for x, y from

$$𝑓_1 (𝑥,𝑦)=𝑦−1/2 (𝑒^{(𝑥/2)}+𝑒^{(−𝑥/2)} )=0 \\ 𝑓_2 (𝑥,𝑦)=9𝑥^2+25𝑦^2−225=0$$

Tutorial: MATLAB

Create MATLAB program for solving a system of non-linear equations

Download the tutorial source file and fill in the blanks.

• MATLAB tutorial source file : TU_SystemNonlinear.zip

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1) Define functions that returns vector F(x) and matrix J(x).

Matrix myFuncEx1(Matrix X); // X: vector in. Returns Vector F (nx1)

Matrix myJacobEx1(Matrix X); // X: vector in. Returns Matrix J (nxn)

2) Define a system non-linear solver

Matrix nonlinearSys(Matrix Func(Matrix _Z), Matrix Jacob(Matrix _Z), Matrix _Z0, double tol);

returns solution vector XN (nx1)

3) Then, solve the example problem

Tutorial: C-Programming

1. Create a new project “ TU_SystemNonlinear” with Visual Studio, under the directory \NP\tutorial\

2. Download the tutorial source file from

• C-program tutorial source file : TU_SystemNonlinear_student.cpp

1. Add the downloaded source file under the project folder.

2. Fill-in the blanks

Problem 2

Solve for the 3-DOF transformation, angle (θ) and translation T=[Δx, Δy], to move the vehicle to the new pose?

Solution= [θ=30 deg , Δx =100 , Δy= 100 ]