MotionGenesis: Solving nonlinear algebraic equations

Solving one nonlinear algebraic equation

To numerically solve the equation x^2 - cos(x) = 0 for x, type
Note: The argument x = 0.2 provides a starting guess for the solution.

  Variable  x
  Solve( x^2 - cos(x),  x = 0.2 )

Nonlinear equations may have multiple solutions.
The program's solution of x = 0.8241323 depends on the starting guess.
The program frequently converges to a solution close to the starting guess.

To save input (for subsequent re-use) and/or input and output responses, type
Save SolveSampleNonlinearEqn.txt
Save SolveSampleNonlinearEqn.all

MotionGenesis Graph of x^2 - cos(x) versus x

Solving sets of nonlinear algebraic equations

Equations for a circle and sine curve.

x² + y² = 1
y = sin(x)
To numerically solve the previous set of nonlinear equations for x and y, type
Note: The arguments x=3 and x=5 provide a starting guess for the solution.

Variable  x, y
Zero[1] = x^2 +  y^2  -  1
Zero[2] = y - sin(x)
Solve( Zero, x=3, y=5 )

MotionGenesis Numerical solution for finding the intersection of a circle and sine-wave

These nonlinear equations have two solutions.
The program's solution of x = 0.739085 and y = 0.673612 depend on the guess.
The program frequently converges to a solution close to the starting guess.

To save input (for subsequent re-use) and/or input and output responses, type
Save SolveSampleNonlinearEqns.txt
Save SolveSampleNonlinearEqns.all

Solving sets of nonlinear algebraic equations with input

x² + y² = R²
y = A * sin(x)
To numerically solve the previous set of nonlinear equations for x and y, type
Note: Numerical values for A and R are provided in the Input command.

Constant  R, A
Variable  x, y
Zero[1] = x^2 +  y^2  -  R^2
Zero[2] = y - A*sin(x)
Input A=1, R=1
Solve( Zero, x=3, y=5 )

To save input (for subsequent re-use) and/or input and output responses, type
Save SolveSampleNonlinearEqnsWithInput.txt
Save SolveSampleNonlinearEqnsWithInput.all

Generating code to solve nonlinear algebraic equations
MotionGenesis produces highly efficient and symbolically optimized codes.
A simple command file shows how to generate various codes to solve the previous nonlinear equations.
Depending on your license, these deployable codes are independent of MotionGenesis.
Note: Each code outputs results in the file CodeSampleNonlinearEqns.1

Code	Command file	Comments
C	CodeSampleNonlinearEqns.c	Compile and link source code. Modify input values in CodeSampleNonlinearEqns.in Note: Compiled code optimizes for its processor.
Fortran	CodeSampleNonlinearEqns.f	Compile and link source code. Modify input values in CodeSampleNonlinearEqns.in Note: Compiled code optimizes for its processor.
MATLAB®	CodeSampleNonlinearEqns.m	Invoke MATLAB® and type load CodeSampleNonlinearEqns Modify input values in CodeSampleNonlinearEqns.m Note: Interpreted .m codes are slower than compiled codes.

To save input (for subsequent re-use) and/or input and output responses, type
Save CodeSampleNonlinearEqns.txt
Save CodeSampleNonlinearEqns.all