MotionGenesis: Solve linear equations

Solve linear equations

To symbolically solve the set of algebraic equations shown below (which are linear in x and y), type

Variable x, y Eqn[1] = 2*x + 3*y - sin(t) Eqn[2] = 4*x + 5*y - cos(t) Solve( Eqn = 0, x, y )

2 x + 3 y = sin(t)
4 x + 5 y = cos(t)

The response to this Solve command is

-> x = 1.5*cos(t) - 2.5*sin(t) -> y = 2*sin(t) - cos(t)

To save commands (for subsequent re-use) or commands/responses, type

Save MGSolveLinearEqns.txt % Save commands. Save MGSolveLinearEqns.html % Save commands and responses.

Advanced: To write a MATLAB® code to solve for x and y for 0 ≤ t ≤ 4, type

Variable x, y Eqn[1] = 2*x + 3*y - sin(t) Eqn[2] = 4*x + 5*y - cos(t) Output t sec, x meter, y meter Code Algebraic(Eqn = 0, x, y) [t = 0, 4, 1] MGSolveLinearEqns.m

Running the MotionGenesis™-generated .m file produces,

% FILE: MGSolveLinearEqns.1
%
%   t           x           y
% (sec)      (meter)     (meter)

 0.00E+00   1.500E+00  -1.000E+00
 1.00E+00  -1.293E+00   1.143E+00
 2.00E+00  -2.898E+00   2.235E+00
 3.00E+00  -1.838E+00   1.272E+00
 4.00E+00   9.115E-01  -8.560E-01

MotionGenesis™ also does matrix algebra and numerically solves sets of nonlinear equations.