% MotionGenesis file: MGSolveNonlinearEqnContinuouslyA.txt
% Copyright (c) 2024 Motion Genesis LLC.
% Purpose: Continuous solution to the nonlinear algebraic equation:
%          y^4 - 8*y - 0.3*t^2 - 9*sin(t) = 0
% Related: MGSolveNonlinearEqnContinuouslyA.txt
%          MGSolveNonlinearEqnsContinuouslyB.txt
%          MGSolveNonlinearEqnsContinuouslyC.txt
%          MGFigureEightLinkageInverseKinematics.txt
%---------------------------------------------------------------------------
%   For a continuous solution y(t), declare y and its 1st time-derivative.
Variable  y'
eqnToSolve = y^4 - 8*y - 0.3*t^2 - 9*sin(t)
%---------------------------------------------------------------------------
%   Differentiate eqnToSolve to form an equation that is _linear_ in y'.
eqnDt = Dt( eqnToSolve )
%---------------------------------------------------------------------------
%   Calculate the values of y that satisfy eqnToSolve at t = 0.
yValuesAt0 = GetQuarticRoots( Evaluate(eqnToSolve, t=0) = 0,  y )
%---------------------------------------------------------------------------
%   Solve eqnDt = 0 to form an ODE (ordinary differential equation) for y'.
Solve( eqnDt = 0,   y' )
%---------------------------------------------------------------------------
%   Set the initial value for y from one of the quadratic roots at t = 0.
Input  y = yValuesAt0[4] meters
%---------------------------------------------------------------------------
%   List output quantities (for subsequent ODE command).
Output t seconds,  y meters
%---------------------------------------------------------------------------
%   Set numerical integration parameters, solve ODEs, and plot results.
Input  tFinal = 20 seconds,  tStep = 0.02 sec,  absError = 1.0E-07
ODE() MGSolveNonlinearEqnContinuouslyA
Plot  MGSolveNonlinearEqnContinuouslyA.1
%--------------------------------------------------------------------
%   Record input together with responses.
Save  MGSolveNonlinearEqnContinuouslyA.html
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