% MotionGenesis file: MGSolveNonlinearEqnsContinuouslyB.txt
% Copyright (c) 2024 Motion Genesis LLC. All rights reserved.
% Purpose: Continuous solution to the nonlinear algebraic equations:
%          cos(qA) + 2*cos(qB) = 2 + 0.2*cos(t)
%          2*sin(qB) - sin(qA) = 0.3*sin(3*t)
% Related: MGSolveNonlinearEqnContinuouslyA.txt
%          MGSolveNonlinearEqnsContinuouslyB.txt
%          MGSolveNonlinearEqnsContinuouslyC.txt
%          MGFigureEightLinkageInverseKinematics.txt
%-------------------------------------------------------------------------------
Variable  qA', qB'
eqnToSolve[1] = cos(qA) + 2*cos(qB) - 2 - 0.2*cos(t)
eqnToSolve[2] = 2*sin(qB) - sin(qA) - 0.3*sin(3*t)
%-------------------------------------------------------------------------------
%   Differentiate eqnToSolve to form equations that are _linear_ in qA', qB'.
eqnDt = Dt( eqnToSolve )
%-------------------------------------------------------------------------------
%   Solve eqnDt = 0 to form an ODE (ordinary differential equation) for qA' and qB'
Solve( eqnDt = 0,   qA', qB' )
%-------------------------------------------------------------------------------
%   Form a set of equations that govern the values of qA and qB at t = 0.
eqnInitial = Evaluate( eqnToSolve, t = 0 )
%-------------------------------------------------------------------------------
%   Solve the nonlinear equations at t = 0 to set initial values for qA and qB.
%   Since the equations are nonlinear, provide a guess for qA and qB
SolveSetInput( eqnInitial = 0,  qA = 20 degrees,  qB = 60 degrees )
%-------------------------------------------------------------------------------
%   List output quantities (for subsequent ODE command).
Output  t seconds,  qA degrees,  qB degrees
%--------------------------------------------------------------------
%   Set numerical integration parameters and solve ODEs.
Input  tFinal = 8 sec,  tStep = 0.02 sec,  absError = 1.0E-07
ODE()  MGSolveNonlinearEqnsContinuouslyB
%-------------------------------------------------------------------------------
%   Optional: Plot results.
% Plot MGSolveNonlinearEqnsContinuouslyB.1 [1, 2, 3]
%-------------------------------------------------------------------------------
%   Record input together with responses.
Save  MGSolveNonlinearEqnsContinuouslyB.html
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