StationaryHelicopterRetrievalKane.html  (MotionGenesis input/output).
   (1) % MotionGenesis file:  StationaryHelicopterRetrievalKane.txt
   (2) % Problem: Retrieval of capsized fishermen.
   (3) % Copyright (c) 2009 Motion Genesis LLC.  All rights reserved.
   (4) %------------------------------------------------------------
   (5) NewtonianFrame N             % Earth.
   (6) RigidFrame     B             % Cable.
   (7) Particle       Q             % Rescue basket and fishermen.
   (8) %------------------------------------------------------------
   (9) Q.SetMass( m = 100 kg )
   (10) Constant   g = 9.8 m/s^2     % Earth's gravitational acceleration.
   (11) Variable   theta''           % Pendulum swing angle.
   (12) Variable   Tension           % Tension in cable.
   (13) Constant   L0 = 50 m         % Initial cable length.
   (14) Constant   s = 2 m/s         % Rate at which cable is retrieved.
   (15) Specified  L''               % Cable length (varies).
   (16) SetDt( L = L0 - s*t )
-> (17) L = L0 - s*t
-> (18) L' = -s
-> (19) L'' = 0

   (20) %------------------------------------------------------------
   (21) %       Rotation and translation kinematics.
   (22) B.RotateZ( N, theta )
-> (23) B_N = [cos(theta), sin(theta), 0;  -sin(theta), cos(theta), 0;  0, 0, 1]
-> (24) w_B_N> = theta'*Bz>
-> (25) alf_B_N> = theta''*Bz>

   (26) Q.Translate( No, -L*By> )
-> (27) p_No_Q> = -L*By>
-> (28) v_Q_N> = L*theta'*Bx> - L'*By>
-> (29) a_Q_N> = (2*L'*theta'+L*theta'')*Bx> + (L*theta'^2-L'')*By>

   (30) %------------------------------------------------------------
   (31) %       Add relevant contact and distance forces.
   (32) Q.AddForce( -m*g*Ny> + Tension*By> )
-> (33) Force_Q> = Tension*By> - m*g*Ny>

   (34) %------------------------------------------------------------
   (35) %       Form equations of motion using Kane's method.
   (36) SetGeneralizedSpeed( theta' )
   (37) Zero = System.GetDynamicsKane()
-> (38) Zero = [m*L*(g*sin(theta)+2*L'*theta'+L*theta'')]

   (39) Solve( Zero,  theta'' )
-> (40) theta'' = -(g*sin(theta)+2*L'*theta')/L

   (41) %------------------------------------------------------------
   (42) %       Input initial values and numerical integration parameters.
   (43) Input   theta = 1 deg,  theta' = 0 deg/sec
   (44) Input   tFinal = 24.92 sec,  tStep = 0.02 sec
   (45) %------------------------------------------------------------
   (46) %       List output quantities and solve ODEs.
   (47) OutputPlot  t sec,  theta deg
   (48) ODE() StationaryHelicopterRetrievalKane

   (49) %------------------------------------------------------------
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