Solve nonlinear equations (advanced)
Coding nonlinear algebraic equations.
| Equation for circle: | x2 + y2 = R2 |
| Equation for sine curve: | y = A * sin(x) |
To write a MATLAB® code to numerically solve for x and y
for 1 ≤ R ≤ 3,
type
Constant R % Radius of circle.
Constant A = 1 meter % Amplitude of sine wave.
Variable x, y
Eqn[1] = x^2 + y^2 - R^2 % Circle: x^2 + y^2 = R^2
Eqn[2] = y - A*sin(x) % Sine wave: y = A*sin(x)
Input x = 3 meters, y = 3 meters
Output R meters, x meters, y meters
Nonlinear(Eqn = 0, x, y) [R = 1, 3, 0.5] MGSolveNonlinearEqns.m
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C code
MGSolveNonlinearEqns.c |
Compile and link source code.
Modify input values in MGSolveNonlinearEqns.in |
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Fortran code
MGSolveNonlinearEqns.f |
Compile and link source code.
Modify input values in MGSolveNonlinearEqns.in |
|
MATLAB®
MGSolveNonlinearEqns.m |
Invoke MATLAB® and type MGSolveNonlinearEqns
Modify input values in MGSolveNonlinearEqns.m |
One way to run this MATLAB® .m script is to open MATLAB®
and click the "Browse For Folder" icon as shown below:
Browse to your MotionGenesis folder, select it (single click), then click OK (or Open).
The MotionGenesis folder name should appear in the textbox.
In the MATLAB® command window, type MGSolveNonlinearEqns to produce:
% FILE: MGSolveNonlinearEqns.1 % % Residual R x y % (UNITS) (meters) (meters) (meters) 1.221E-15 1.00E+00 7.391E-01 6.736E-01 1.177E-14 1.50E+00 1.181E+00 9.249E-01 3.483E-13 2.00E+00 1.740E+00 9.857E-01 2.209E-13 2.50E+00 2.409E+00 6.689E-01 4.656E-15 3.00E+00 2.997E+00 1.446E-01
Continuous solution of one nonlinear algebraic equation.
Solve for y(t) for 0 ≤ t ≤ 20
Solve for y(t) for 0 ≤ t ≤ 20
y4 - 8*y - 0.3*t2 - 9*sin(t) = 0
Program commands: MGSolveNonlinearEqnContinuouslyA.txt
Program responses: MGSolveNonlinearEqnContinuouslyA.html
Continuous solution of two coupled nonlinear algebraic equations.
Solve for qA(t) and qB(t) for 0 ≤ t ≤ 2.2
Solve for qA(t) and qB(t) for 0 ≤ t ≤ 2.2
cos(qA) + 2*cos(qB) = 2 + 0.2*cos(t)
2*sin(qB) - sin(qA) = 0.3*sin(3*t)
2*sin(qB) - sin(qA) = 0.3*sin(3*t)
Program commands: MGSolveNonlinearEqnsContinuouslyB.txt
Program responses: MGSolveNonlinearEqnsContinuouslyB.html
Continuous solution of two coupled nonlinear algebraic.
Solve for r(t) and θ(t) for 0 ≤ t ≤ 7
Solve for r(t) and θ(t) for 0 ≤ t ≤ 7
x = r*cos(θ) where x = cos(1.2*t)
y = r*sin(θ) where y = sin(t)
y = r*sin(θ) where y = sin(t)
Program commands: MGSolveNonlinearEqnsContinuouslyC.txt
Program responses: MGSolveNonlinearEqnsContinuouslyC.html
MotionGenesis™ also does vector algebra, matrix algebra and solves sets of linear equations and ODEs (ordinary differential equations).
Simpler:
Check out nonlinear equations basics.