Solve nonlinear equations (basics)
Solve one nonlinear algebraic equation.
To numerically solve the nonlinear equation x^2 - cos(x) = 0, type
Variable x
Solve( x^2 - cos(x) = 0, x = 0.2 ) % x = 0.2 is a guess.
| If you guess | x = 0.2, | Solves to x = 0.82413 |
| If you guess | x = -9, | Solves to x = -0.82413 |
To save commands (for subsequent re-use) or commands/responses, type
Save MGSolveNonlinearEqn.txt % Save commands.
Save MGSolveNonlinearEqn.html % Save commands and responses.
Solve sets of nonlinear algebraic equations.
| Equation for circle: | x2 + y2 = R2 |
| Equation for sine curve: | y = A * sin(x) |
To numerically solve these equations for x and y, type
Clear (to clear the previous workspace),
then type
Constant R = 1 meter, A = 1 meter
Variable x, y
eqns[1] = x^2 + y^2 - R^2 % Circle
eqns[2] = y - A*sin(x) % Sine wave
Solve( eqns = 0, x = 3, y = 5 )
Note: The arguments x = 3 and
y = 5 are a guess for the solution.
The two solutions to these nonlinear equations depend on your guess, e.g.,
| Guess | x = 3, | y = 5, | -> | x = 0.7391, | y = 0.6736 |
| Guess | x = -2, | y = -2, | -> | x = -0.7391, | y = -0.6736 |
To save commands (for subsequent re-use) or commands/responses, type
Save MGSolveNonlinearEqns.txt % Commands.
Save MGSolveNonlinearEqns.html % Commands and responses.
MotionGenesis™ also does vector algebra, matrix algebra and solves sets of linear equations and ODEs (ordinary differential equations).
Advanced:
Auto-generate MATLAB® C, etc., codes to solve nonlinear equations and/or
determine continuous
solutions of nonlinear equations.