MotionGenesis: MGSpinStability3DRigidBodyKane.html

MGSpinStability3DRigidBodyKane.html (MotionGenesis input/output).
   (1) % MotionGenesis file:  MGSpinStability3DRigidBodyKane.txt
   (2) % Copyright (c) 2009 Motion Genesis LLC.  All rights reserved.
   (3) % Purpose: Spin stability of rigid body (books, footballs, aircraft).
   (4) %-------------------------------------------------------------------
   (5) %       Physical objects
   (6) NewtonianFrame  N
   (7) RigidBody       B
   (8) %-------------------------------------------------------------------
   (9) Variable   wx',  wy',  wz'         % Angular velocity measures
   (10) Constant   b = 0.0 N*m*s/rad       % Viscous damping constant
   (11) B.SetMassInertia( m = 0.4 kg,  Ixx = 1 kg*m^2,  Iyy = 2 kg*m^2,  Izz = 3 kg*m^2 )
   (12) %-------------------------------------------------------------------
   (13) %       Rotational and translational kinematics.
   (14) B.SetAngularVelocityAcceleration( N,  wx*Bx> + wy*By> + wz*Bz> )
-> (15) w_B_N> = wx*Bx> + wy*By> + wz*Bz>
-> (16) alf_B_N> = wx'*Bx> + wy'*By> + wz'*Bz>

   (17) Bcm.SetVelocity( N, 0> )
-> (18) v_Bcm_N> = 0>

   (19) %-------------------------------------------------------------------
   (20) %       Add torques.
   (21) B.AddTorque( -b * B.GetAngularVelocity(N) )
-> (22) Torque_B> = -b*wx*Bx> - b*wy*By> - b*wz*Bz>

   (23) %-------------------------------------------------------------------
   (24) %       Form Kane's equations of motion.
   (25) SetGeneralizedSpeed( wx,  wy,  wz )
   (26) Dynamics = System.GetDynamicsKane()
-> (27) Dynamics[1] = b*wx + Ixx*wx' - (Iyy-Izz)*wy*wz
-> (28) Dynamics[2] = b*wy + (Ixx-Izz)*wx*wz + Iyy*wy'
-> (29) Dynamics[3] = b*wz + Izz*wz' - (Ixx-Iyy)*wx*wy

   (30) Solve( Dynamics = 0,   wx',  wy',  wz'  )
-> (31) wx' = -(b*wx-(Iyy-Izz)*wy*wz)/Ixx
-> (32) wy' = -(b*wy+(Ixx-Izz)*wx*wz)/Iyy
-> (33) wz' = -(b*wz-(Ixx-Iyy)*wx*wy)/Izz

   (34) %-------------------------------------------------------------------
   (35) %       Numerical integration parameters and initial values.
   (36) Input  tFinal = 4 sec,  tStep = 0.02 sec,  absError = 1.0E-08
   (37) Input  wx  = 0.2 rad/sec,   wy = 7.0 rad/sec,  wz = 0.2 rad/sec
   (38) %-------------------------------------------------------------------
   (39) %       Form output quantities and solve ODEs.
   (40) H> = B.GetAngularMomentum( Bcm )
-> (41) H> = Ixx*wx*Bx> + Iyy*wy*By> + Izz*wz*Bz>

   (42) Hmag = GetMagnitude( H> )
-> (43) Hmag = sqrt(Ixx^2*wx^2+Iyy^2*wy^2+Izz^2*wz^2)

   (44) Wmag = B.GetAngularSpeed( N )
-> (45) Wmag = sqrt(wx^2+wy^2+wz^2)

   (46) theta = acos( Dot( H>, B.GetAngularVelocity(N) ) / (Hmag * Wmag) )
-> (47) theta = acos((Ixx*wx^2+Iyy*wy^2+Izz*wz^2)/(Hmag*Wmag))

   (48) OutputPlot  t sec,  wx rad/sec,  wy rad/sec,  wz rad/sec
   (49) OutputPlot  t sec,  theta deg,  Hmag kg*m^2/sec^2
   (50) ODE()  MGSpinStability3DRigidBodyKane

   (51) %-------------------------------------------------------------------