X-Git-Url: https://git.mxchange.org/?a=blobdiff_plain;f=src%2FFDM%2FJSBSim%2Fmodels%2FFGPropagate.cpp;h=3c77bca282af8e5df2c38680b08efdd9924d064a;hb=024ef128e3395e8c0e32b360abe19b4d345e4f80;hp=9bd50289882d378cae31575ecb69f13b59e308a2;hpb=3e0489bd910620e5d34e33d231c55135daeb2543;p=flightgear.git diff --git a/src/FDM/JSBSim/models/FGPropagate.cpp b/src/FDM/JSBSim/models/FGPropagate.cpp index 9bd502898..3c77bca28 100644 --- a/src/FDM/JSBSim/models/FGPropagate.cpp +++ b/src/FDM/JSBSim/models/FGPropagate.cpp @@ -48,6 +48,16 @@ COMMENTS, REFERENCES, and NOTES Wiley & Sons, 1979 ISBN 0-471-03032-5 [5] Bernard Etkin, "Dynamics of Flight, Stability and Control", Wiley & Sons, 1982 ISBN 0-471-08936-2 +[6] S. Buss, "Accurate and Efficient Simulation of Rigid Body Rotations", + Technical Report, Department of Mathematics, University of California, + San Diego, 1999 +[7] Barker L.E., Bowles R.L. and Williams L.H., "Development and Application of + a Local Linearization Algorithm for the Integration of Quaternion Rate + Equations in Real-Time Flight Simulation Problems", NASA TN D-7347, + December 1973 +[8] Phillips W.F, Hailey C.E and Gebert G.A, "Review of Attitude Representations + Used for Aircraft Kinematics", Journal Of Aircraft Vol. 38, No. 4, + July-August 2001 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% INCLUDES @@ -56,53 +66,45 @@ INCLUDES #include #include #include +#include #include "FGPropagate.h" +#include "FGGroundReactions.h" #include "FGFDMExec.h" -#include "FGState.h" -#include "FGAircraft.h" -#include "FGMassBalance.h" -#include "FGInertial.h" #include "input_output/FGPropertyManager.h" using namespace std; namespace JSBSim { -static const char *IdSrc = "$Id$"; +static const char *IdSrc = "$Id: FGPropagate.cpp,v 1.105 2012/03/26 21:26:11 bcoconni Exp $"; static const char *IdHdr = ID_PROPAGATE; /*%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% CLASS IMPLEMENTATION %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%*/ -FGPropagate::FGPropagate(FGFDMExec* fdmex) : FGModel(fdmex) +FGPropagate::FGPropagate(FGFDMExec* fdmex) + : FGModel(fdmex), + VehicleRadius(0) { Debug(0); Name = "FGPropagate"; - last2_vPQRdot.InitMatrix(); - last_vPQRdot.InitMatrix(); - vPQRdot.InitMatrix(); - - last2_vQtrndot = FGQuaternion(0,0,0); - last_vQtrndot = FGQuaternion(0,0,0); - vQtrndot = FGQuaternion(0,0,0); - - last2_vUVWdot.InitMatrix(); - last_vUVWdot.InitMatrix(); - vUVWdot.InitMatrix(); - - last2_vLocationDot.InitMatrix(); - last_vLocationDot.InitMatrix(); - vLocationDot.InitMatrix(); - - vOmegaLocal.InitMatrix(); - - integrator_rotational_rate = eAdamsBashforth2; - integrator_translational_rate = eTrapezoidal; - integrator_rotational_position = eAdamsBashforth2; - integrator_translational_position = eTrapezoidal; + vInertialVelocity.InitMatrix(); + + /// These define the indices use to select the various integrators. + // eNone = 0, eRectEuler, eTrapezoidal, eAdamsBashforth2, eAdamsBashforth3, eAdamsBashforth4}; + + integrator_rotational_rate = eRectEuler; + integrator_translational_rate = eAdamsBashforth2; + integrator_rotational_position = eRectEuler; + integrator_translational_position = eAdamsBashforth3; + + VState.dqPQRidot.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqUVWidot.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqInertialVelocity.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqQtrndot.resize(4, FGQuaternion(0.0,0.0,0.0)); bind(); Debug(0); @@ -119,37 +121,21 @@ FGPropagate::~FGPropagate(void) bool FGPropagate::InitModel(void) { - if (!FGModel::InitModel()) return false; - // For initialization ONLY: - SeaLevelRadius = LocalTerrainRadius = Inertial->GetRefRadius(); - - VState.vLocation.SetRadius( LocalTerrainRadius + 4.0 ); - VState.vLocation.SetEllipse(Inertial->GetSemimajor(), Inertial->GetSemiminor()); - vOmega = FGColumnVector3( 0.0, 0.0, Inertial->omega() ); // Earth rotation vector - - last2_vPQRdot.InitMatrix(); - last_vPQRdot.InitMatrix(); - vPQRdot.InitMatrix(); - - last2_vQtrndot = FGQuaternion(0,0,0); - last_vQtrndot = FGQuaternion(0,0,0); - vQtrndot = FGQuaternion(0,0,0); - - last2_vUVWdot.InitMatrix(); - last_vUVWdot.InitMatrix(); - vUVWdot.InitMatrix(); - - last2_vLocationDot.InitMatrix(); - last_vLocationDot.InitMatrix(); - vLocationDot.InitMatrix(); - - vOmegaLocal.InitMatrix(); - - integrator_rotational_rate = eAdamsBashforth2; - integrator_translational_rate = eTrapezoidal; - integrator_rotational_position = eAdamsBashforth2; - integrator_translational_position = eTrapezoidal; + VState.vLocation.SetEllipse(in.SemiMajor, in.SemiMinor); + VState.vLocation.SetAltitudeAGL(4.0, FDMExec->GetSimTime()); + + vInertialVelocity.InitMatrix(); + + VState.dqPQRidot.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqUVWidot.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqInertialVelocity.resize(4, FGColumnVector3(0.0,0.0,0.0)); + VState.dqQtrndot.resize(4, FGColumnVector3(0.0,0.0,0.0)); + + integrator_rotational_rate = eRectEuler; + integrator_translational_rate = eAdamsBashforth2; + integrator_rotational_position = eRectEuler; + integrator_translational_position = eAdamsBashforth3; return true; } @@ -158,54 +144,56 @@ bool FGPropagate::InitModel(void) void FGPropagate::SetInitialState(const FGInitialCondition *FGIC) { - SetSeaLevelRadius(FGIC->GetSeaLevelRadiusFtIC()); - SetTerrainElevation(FGIC->GetTerrainElevationFtIC()); + // Initialize the State Vector elements and the transformation matrices // Set the position lat/lon/radius - VState.vLocation.SetPosition( FGIC->GetLongitudeRadIC(), - FGIC->GetLatitudeRadIC(), - FGIC->GetAltitudeASLFtIC() + FGIC->GetSeaLevelRadiusFtIC() ); + VState.vLocation = FGIC->GetPosition(); - VehicleRadius = GetRadius(); - radInv = 1.0/VehicleRadius; + Ti2ec = VState.vLocation.GetTi2ec(); // ECI to ECEF transform + Tec2i = Ti2ec.Transposed(); // ECEF to ECI frame transform - // Set the Orientation from the euler angles - VState.vQtrn = FGQuaternion( FGIC->GetPhiRadIC(), - FGIC->GetThetaRadIC(), - FGIC->GetPsiRadIC() ); + VState.vInertialPosition = Tec2i * VState.vLocation; - // Set the velocities in the instantaneus body frame - VState.vUVW = FGColumnVector3( FGIC->GetUBodyFpsIC(), - FGIC->GetVBodyFpsIC(), - FGIC->GetWBodyFpsIC() ); + UpdateLocationMatrices(); - // Set the angular velocities in the instantaneus body frame. - VState.vPQR = FGColumnVector3( FGIC->GetPRadpsIC(), - FGIC->GetQRadpsIC(), - FGIC->GetRRadpsIC() ); + // Set the orientation from the euler angles (is normalized within the + // constructor). The Euler angles represent the orientation of the body + // frame relative to the local frame. + VState.qAttitudeLocal = FGIC->GetOrientation(); + + VState.qAttitudeECI = Ti2l.GetQuaternion()*VState.qAttitudeLocal; + UpdateBodyMatrices(); + + // Set the velocities in the instantaneus body frame + VState.vUVW = FGIC->GetUVWFpsIC(); // Compute the local frame ECEF velocity - vVel = GetTb2l()*VState.vUVW; - - // Finally, make sure that the quaternion stays normalized. - VState.vQtrn.Normalize(); - - // Recompute the LocalTerrainRadius. - RecomputeLocalTerrainRadius(); - - // These local copies of the transformation matrices are for use for - // initial conditions only. - - Tl2b = GetTl2b(); // local to body frame transform - Tb2l = Tl2b.Transposed(); // body to local frame transform - Tl2ec = GetTl2ec(); // local to ECEF transform - Tec2l = Tl2ec.Transposed(); // ECEF to local frame transform - Tec2b = Tl2b * Tec2l; // ECEF to body frame transform - Tb2ec = Tec2b.Transposed(); // body to ECEF frame tranform - Ti2ec = GetTi2ec(); // ECI to ECEF transform - Tec2i = Ti2ec.Transposed(); // ECEF to ECI frame transform - Ti2b = Tec2b*Ti2ec; // ECI to body frame transform - Tb2i = Ti2b.Transposed(); // body to ECI frame transform + vVel = Tb2l * VState.vUVW; + + // Compute local terrain velocity + RecomputeLocalTerrainVelocity(); + VehicleRadius = GetRadius(); + + // Set the angular velocities of the body frame relative to the ECEF frame, + // expressed in the body frame. + VState.vPQR = FGIC->GetPQRRadpsIC(); + + VState.vPQRi = VState.vPQR + Ti2b * in.vOmegaPlanet; + + CalculateInertialVelocity(); // Translational position derivative +} + +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +// Initialize the past value deques + +void FGPropagate::InitializeDerivatives() +{ + for (int i=0; i<4; i++) { + VState.dqPQRidot[i] = in.vPQRidot; + VState.dqUVWidot[i] = in.vUVWidot; + VState.dqInertialVelocity[i] = VState.vInertialVelocity; + VState.dqQtrndot[i] = in.vQtrndot; + } } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -221,296 +209,388 @@ This propagation is done using the current state values and current derivatives. Based on these values we compute an approximation to the state values for (now + dt). -In the code below, variables named beginning with a small "v" refer to a +In the code below, variables named beginning with a small "v" refer to a a column vector, variables named beginning with a "T" refer to a transformation matrix. ECEF refers to Earth Centered Earth Fixed. ECI refers to Earth Centered Inertial. */ -bool FGPropagate::Run(void) +bool FGPropagate::Run(bool Holding) { - if (FGModel::Run()) return true; // Fast return if we have nothing to do ... - if (FDMExec->Holding()) return false; + if (FGModel::Run(Holding)) return true; // Fast return if we have nothing to do ... + if (Holding) return false; - RunPreFunctions(); + double dt = in.DeltaT * rate; // The 'stepsize' - RecomputeLocalTerrainRadius(); + // Propagate rotational / translational velocity, angular /translational position, respectively. - // Calculate current aircraft radius from center of planet + Integrate(VState.qAttitudeECI, in.vQtrndot, VState.dqQtrndot, dt, integrator_rotational_position); + Integrate(VState.vPQRi, in.vPQRidot, VState.dqPQRidot, dt, integrator_rotational_rate); + Integrate(VState.vInertialPosition, VState.vInertialVelocity, VState.dqInertialVelocity, dt, integrator_translational_position); + Integrate(VState.vInertialVelocity, in.vUVWidot, VState.dqUVWidot, dt, integrator_translational_rate); - VehicleRadius = GetRadius(); - radInv = 1.0/VehicleRadius; - - // These local copies of the transformation matrices are for use this - // pass through Run() only. - - Tl2b = GetTl2b(); // local to body frame transform - Tb2l = Tl2b.Transposed(); // body to local frame transform - Tl2ec = GetTl2ec(); // local to ECEF transform - Tec2l = Tl2ec.Transposed(); // ECEF to local frame transform - Tec2b = Tl2b * Tec2l; // ECEF to body frame transform - Tb2ec = Tec2b.Transposed(); // body to ECEF frame tranform - Ti2ec = GetTi2ec(); // ECI to ECEF transform - Tec2i = Ti2ec.Transposed(); // ECEF to ECI frame transform - Ti2b = Tec2b*Ti2ec; // ECI to body frame transform - Tb2i = Ti2b.Transposed(); // body to ECI frame transform + // CAUTION : the order of the operations below is very important to get transformation + // matrices that are consistent with the new state of the vehicle + + // 1. Update the Earth position angle (EPA) + VState.vLocation.IncrementEarthPositionAngle(in.vOmegaPlanet(eZ)*(in.DeltaT*rate)); + + // 2. Update the Ti2ec and Tec2i transforms from the updated EPA + Ti2ec = VState.vLocation.GetTi2ec(); // ECI to ECEF transform + Tec2i = Ti2ec.Transposed(); // ECEF to ECI frame transform + + // 3. Update the location from the updated Ti2ec and inertial position + VState.vLocation = Ti2ec*VState.vInertialPosition; + + // 4. Update the other "Location-based" transformation matrices from the updated + // vLocation vector. + UpdateLocationMatrices(); + + // 5. Update the "Orientation-based" transformation matrices from the updated + // orientation quaternion and vLocation vector. + UpdateBodyMatrices(); + + // Translational position derivative (velocities are integrated in the inertial frame) + CalculateUVW(); + + // Set auxilliary state variables + RecomputeLocalTerrainVelocity(); + VehicleRadius = GetRadius(); // Calculate current aircraft radius from center of planet + + VState.vPQR = VState.vPQRi - Ti2b * in.vOmegaPlanet; + + VState.qAttitudeLocal = Tl2b.GetQuaternion(); // Compute vehicle velocity wrt ECEF frame, expressed in Local horizontal frame. vVel = Tb2l * VState.vUVW; - // Inertial angular velocity measured in the body frame. - vPQRi = VState.vPQR + Tec2b*vOmega; + Debug(2); + return false; +} - // Calculate state derivatives - CalculatePQRdot(); // Angular rate derivative - CalculateUVWdot(); // Translational rate derivative - CalculateQuatdot(); // Angular orientation derivative - CalculateLocationdot(); // Translational position derivative +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + // Transform the velocity vector of the body relative to the origin (Earth + // center) to be expressed in the inertial frame, and add the vehicle velocity + // contribution due to the rotation of the planet. + // Reference: See Stevens and Lewis, "Aircraft Control and Simulation", + // Second edition (2004), eqn 1.5-16c (page 50) - // Integrate to propagate the state +void FGPropagate::CalculateInertialVelocity(void) +{ + VState.vInertialVelocity = Tb2i * VState.vUVW + (in.vOmegaPlanet * VState.vInertialPosition); +} - double dt = State->Getdt()*rate; // The 'stepsize' +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + // Transform the velocity vector of the inertial frame to be expressed in the + // body frame relative to the origin (Earth center), and substract the vehicle + // velocity contribution due to the rotation of the planet. - // Propagate rotational velocity +void FGPropagate::CalculateUVW(void) +{ + VState.vUVW = Ti2b * (VState.vInertialVelocity - (in.vOmegaPlanet * VState.vInertialPosition)); +} - switch(integrator_rotational_rate) { - case eRectEuler: VState.vPQR += dt*vPQRdot; - break; - case eTrapezoidal: VState.vPQR += 0.5*dt*(vPQRdot + last_vPQRdot); - break; - case eAdamsBashforth2: VState.vPQR += dt*(1.5*vPQRdot - 0.5*last_vPQRdot); - break; - case eAdamsBashforth3: VState.vPQR += (1/12.0)*dt*(23.0*vPQRdot - 16.0*last_vPQRdot + 5.0*last2_vPQRdot); - break; - case eNone: // do nothing, freeze angular rate - break; - } - - // Propagate translational velocity +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - switch(integrator_translational_rate) { - case eRectEuler: VState.vUVW += dt*vUVWdot; +void FGPropagate::Integrate( FGColumnVector3& Integrand, + FGColumnVector3& Val, + deque & ValDot, + double dt, + eIntegrateType integration_type) +{ + ValDot.push_front(Val); + ValDot.pop_back(); + + switch(integration_type) { + case eRectEuler: Integrand += dt*ValDot[0]; + break; + case eTrapezoidal: Integrand += 0.5*dt*(ValDot[0] + ValDot[1]); break; - case eTrapezoidal: VState.vUVW += 0.5*dt*(vUVWdot + last_vUVWdot); + case eAdamsBashforth2: Integrand += dt*(1.5*ValDot[0] - 0.5*ValDot[1]); break; - case eAdamsBashforth2: VState.vUVW += dt*(1.5*vUVWdot - 0.5*last_vUVWdot); + case eAdamsBashforth3: Integrand += (1/12.0)*dt*(23.0*ValDot[0] - 16.0*ValDot[1] + 5.0*ValDot[2]); break; - case eAdamsBashforth3: VState.vUVW += (1/12.0)*dt*(23.0*vUVWdot - 16.0*last_vUVWdot + 5.0*last2_vUVWdot); + case eAdamsBashforth4: Integrand += (1/24.0)*dt*(55.0*ValDot[0] - 59.0*ValDot[1] + 37.0*ValDot[2] - 9.0*ValDot[3]); break; case eNone: // do nothing, freeze translational rate break; + default: + break; } +} - // Propagate angular position +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - switch(integrator_rotational_position) { - case eRectEuler: VState.vQtrn += dt*vQtrndot; - break; - case eTrapezoidal: VState.vQtrn += 0.5*dt*(vQtrndot + last_vQtrndot); - break; - case eAdamsBashforth2: VState.vQtrn += dt*(1.5*vQtrndot - 0.5*last_vQtrndot); - break; - case eAdamsBashforth3: VState.vQtrn += (1/12.0)*dt*(23.0*vQtrndot - 16.0*last_vQtrndot + 5.0*last2_vQtrndot); +void FGPropagate::Integrate( FGQuaternion& Integrand, + FGQuaternion& Val, + deque & ValDot, + double dt, + eIntegrateType integration_type) +{ + ValDot.push_front(Val); + ValDot.pop_back(); + + switch(integration_type) { + case eRectEuler: Integrand += dt*ValDot[0]; break; - case eNone: // do nothing, freeze angular position + case eTrapezoidal: Integrand += 0.5*dt*(ValDot[0] + ValDot[1]); break; - } - - // Propagate translational position - - switch(integrator_translational_position) { - case eRectEuler: VState.vLocation += dt*vLocationDot; + case eAdamsBashforth2: Integrand += dt*(1.5*ValDot[0] - 0.5*ValDot[1]); break; - case eTrapezoidal: VState.vLocation += 0.5*dt*(vLocationDot + last_vLocationDot); + case eAdamsBashforth3: Integrand += (1/12.0)*dt*(23.0*ValDot[0] - 16.0*ValDot[1] + 5.0*ValDot[2]); break; - case eAdamsBashforth2: VState.vLocation += dt*(1.5*vLocationDot - 0.5*last_vLocationDot); + case eAdamsBashforth4: Integrand += (1/24.0)*dt*(55.0*ValDot[0] - 59.0*ValDot[1] + 37.0*ValDot[2] - 9.0*ValDot[3]); break; - case eAdamsBashforth3: VState.vLocation += (1/12.0)*dt*(23.0*vLocationDot - 16.0*last_vLocationDot + 5.0*last2_vLocationDot); + case eBuss1: + { + // This is the first order method as described in Samuel R. Buss paper[6]. + // The formula from Buss' paper is transposed below to quaternions and is + // actually the exact solution of the quaternion differential equation + // qdot = 1/2*w*q when w is constant. + Integrand = Integrand * QExp(0.5 * dt * VState.vPQRi); + } + return; // No need to normalize since the quaternion exponential is always normal + case eBuss2: + { + // This is the 'augmented second-order method' from S.R. Buss paper [6]. + // Unlike Runge-Kutta or Adams-Bashforth, it is a one-pass second-order + // method (see reference [6]). + FGColumnVector3 wi = VState.vPQRi; + FGColumnVector3 wdoti = in.vPQRidot; + FGColumnVector3 omega = wi + 0.5*dt*wdoti + dt*dt/12.*wdoti*wi; + Integrand = Integrand * QExp(0.5 * dt * omega); + } + return; // No need to normalize since the quaternion exponential is always normal + case eLocalLinearization: + { + // This is the local linearization algorithm of Barker et al. (see ref. [7]) + // It is also a one-pass second-order method. The code below is based on the + // more compact formulation issued from equation (107) of ref. [8]. The + // constants C1, C2, C3 and C4 have the same value than those in ref. [7] pp. 11 + FGColumnVector3 wi = 0.5 * VState.vPQRi; + FGColumnVector3 wdoti = 0.5 * in.vPQRidot; + double omegak2 = DotProduct(VState.vPQRi, VState.vPQRi); + double omegak = omegak2 > 1E-6 ? sqrt(omegak2) : 1E-6; + double rhok = 0.5 * dt * omegak; + double C1 = cos(rhok); + double C2 = 2.0 * sin(rhok) / omegak; + double C3 = 4.0 * (1.0 - C1) / (omegak*omegak); + double C4 = 4.0 * (dt - C2) / (omegak*omegak); + FGColumnVector3 Omega = C2*wi + C3*wdoti + C4*wi*wdoti; + FGQuaternion q; + + q(1) = C1 - C4*DotProduct(wi, wdoti); + q(2) = Omega(eP); + q(3) = Omega(eQ); + q(4) = Omega(eR); + + Integrand = Integrand * q; + + /* Cross check with ref. [7] pp.11-12 formulas and code pp. 20 + double pk = VState.vPQRi(eP); + double qk = VState.vPQRi(eQ); + double rk = VState.vPQRi(eR); + double pdotk = in.vPQRidot(eP); + double qdotk = in.vPQRidot(eQ); + double rdotk = in.vPQRidot(eR); + double Ap = -0.25 * (pk*pdotk + qk*qdotk + rk*rdotk); + double Bp = 0.25 * (pk*qdotk - qk*pdotk); + double Cp = 0.25 * (pdotk*rk - pk*rdotk); + double Dp = 0.25 * (qk*rdotk - qdotk*rk); + double C2p = sin(rhok) / omegak; + double C3p = 2.0 * (1.0 - cos(rhok)) / (omegak*omegak); + double H = C1 + C4 * Ap; + double G = -C2p*rk - C3p*rdotk + C4*Bp; + double J = C2p*qk + C3p*qdotk - C4*Cp; + double K = C2p*pk + C3p*pdotk - C4*Dp; + + cout << "q: " << q << endl; + + // Warning! In the paper of Barker et al. the quaternion components are not + // ordered the same way as in JSBSim (see equations (2) and (3) of ref. [7] + // as well as the comment just below equation (3)) + cout << "FORTRAN: " << H << " , " << K << " , " << J << " , " << -G << endl;*/ + } + break; // The quaternion q is not normal so the normalization needs to be done. + case eNone: // do nothing, freeze rotational rate break; - case eNone: // do nothing, freeze translational position + default: break; } - - // Set past values - - last2_vPQRdot = last_vPQRdot; - last_vPQRdot = vPQRdot; - - last2_vUVWdot = last_vUVWdot; - last_vUVWdot = vUVWdot; - - last2_vQtrndot = last_vQtrndot; - last_vQtrndot = vQtrndot; - - last2_vLocationDot = last_vLocationDot; - last_vLocationDot = vLocationDot; - - RunPreFunctions(); - Debug(2); - return false; + Integrand.Normalize(); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -// Compute body frame rotational accelerations based on the current body moments -// -// vPQRdot is the derivative of the absolute angular velocity of the vehicle -// (body rate with respect to the inertial frame), expressed in the body frame, -// where the derivative is taken in the body frame. -// J is the inertia matrix -// Jinv is the inverse inertia matrix -// vMoments is the moment vector in the body frame -// vPQRi is the total inertial angular velocity of the vehicle -// expressed in the body frame. -// Reference: See Stevens and Lewis, "Aircraft Control and Simulation", -// Second edition (2004), eqn 1.5-16e (page 50) - -void FGPropagate::CalculatePQRdot(void) -{ - const FGColumnVector3& vMoments = Aircraft->GetMoments(); // current moments - const FGMatrix33& J = MassBalance->GetJ(); // inertia matrix - const FGMatrix33& Jinv = MassBalance->GetJinv(); // inertia matrix inverse - - // Compute body frame rotational accelerations based on the current body - // moments and the total inertial angular velocity expressed in the body - // frame. - vPQRdot = Jinv*(vMoments - vPQRi*(J*vPQRi)); +void FGPropagate::UpdateLocationMatrices(void) +{ + Tl2ec = VState.vLocation.GetTl2ec(); // local to ECEF transform + Tec2l = Tl2ec.Transposed(); // ECEF to local frame transform + Ti2l = VState.vLocation.GetTi2l(); // ECI to local frame transform + Tl2i = Ti2l.Transposed(); // local to ECI transform } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -// Compute the quaternion orientation derivative -// -// vQtrndot is the quaternion derivative. -// Reference: See Stevens and Lewis, "Aircraft Control and Simulation", -// Second edition (2004), eqn 1.5-16b (page 50) -void FGPropagate::CalculateQuatdot(void) +void FGPropagate::UpdateBodyMatrices(void) { - vOmegaLocal.InitMatrix( radInv*vVel(eEast), - -radInv*vVel(eNorth), - -radInv*vVel(eEast)*VState.vLocation.GetTanLatitude() ); - - // Compute quaternion orientation derivative on current body rates - vQtrndot = VState.vQtrn.GetQDot( VState.vPQR - Tl2b*vOmegaLocal); + Ti2b = VState.qAttitudeECI.GetT(); // ECI to body frame transform + Tb2i = Ti2b.Transposed(); // body to ECI frame transform + Tl2b = Ti2b * Tl2i; // local to body frame transform + Tb2l = Tl2b.Transposed(); // body to local frame transform + Tec2b = Ti2b * Tec2i; // ECEF to body frame transform + Tb2ec = Tec2b.Transposed(); // body to ECEF frame tranform } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -// This set of calculations results in the body frame accelerations being -// computed. -// Reference: See Stevens and Lewis, "Aircraft Control and Simulation", -// Second edition (2004), eqn 1.5-16d (page 50) - -void FGPropagate::CalculateUVWdot(void) -{ - double mass = MassBalance->GetMass(); // mass - const FGColumnVector3& vForces = Aircraft->GetForces(); // current forces - const FGColumnVector3 vGravAccel( 0.0, 0.0, Inertial->GetGAccel(VehicleRadius) ); +void FGPropagate::SetInertialOrientation(const FGQuaternion& Qi) { + VState.qAttitudeECI = Qi; + VState.qAttitudeECI.Normalize(); + UpdateBodyMatrices(); + VState.qAttitudeLocal = Tl2b.GetQuaternion(); +} - // Begin to compute body frame accelerations based on the current body forces - vUVWdot = vForces/mass - VState.vPQR * VState.vUVW; +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - // Include Coriolis acceleration. - vUVWdot -= 2.0 * (Ti2b *vOmega) * VState.vUVW; +void FGPropagate::SetInertialVelocity(const FGColumnVector3& Vi) { + VState.vInertialVelocity = Vi; + CalculateUVW(); + vVel = Tb2l * VState.vUVW; +} - // Include Centrifugal acceleration. - if (!GroundReactions->GetWOW()) { - vUVWdot -= Ti2b*(vOmega*(vOmega*(Tec2i*VState.vLocation))); - } +//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - // Include Gravitation accel - FGColumnVector3 gravAccel = Tl2b*vGravAccel; - vUVWdot += gravAccel; +void FGPropagate::SetInertialRates(const FGColumnVector3& vRates) { + VState.vPQRi = Ti2b * vRates; + VState.vPQR = VState.vPQRi - Ti2b * in.vOmegaPlanet; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -void FGPropagate::CalculateLocationdot(void) +void FGPropagate::RecomputeLocalTerrainVelocity() { - // Transform the vehicle velocity relative to the ECEF frame, expressed - // in the body frame, to be expressed in the ECEF frame. - vLocationDot = Tb2ec * VState.vUVW; - - // Now, transform the velocity vector of the body relative to the origin (Earth - // center) to be expressed in the inertial frame, and add the vehicle velocity - // contribution due to the rotation of the planet. The above velocity is only - // relative to the rotating ECEF frame. - // Reference: See Stevens and Lewis, "Aircraft Control and Simulation", - // Second edition (2004), eqn 1.5-16c (page 50) - - vInertialVelocity = Tec2i * vLocationDot + (vOmega * (Tec2i * VState.vLocation)); + FGLocation contact; + FGColumnVector3 normal; + VState.vLocation.GetContactPoint(FDMExec->GetSimTime(), contact, normal, + LocalTerrainVelocity, LocalTerrainAngularVelocity); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -void FGPropagate::RecomputeLocalTerrainRadius(void) +void FGPropagate::SetTerrainElevation(double terrainElev) { - double t = State->Getsim_time(); - - // Get the LocalTerrain radius. - FGLocation contactloc; - FGColumnVector3 dv; - FDMExec->GetGroundCallback()->GetAGLevel(t, VState.vLocation, contactloc, dv, dv); - LocalTerrainRadius = contactloc.GetRadius(); + double radius = terrainElev + VState.vLocation.GetSeaLevelRadius(); + FDMExec->GetGroundCallback()->SetTerrainGeoCentRadius(radius); } + //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -void FGPropagate::SetTerrainElevation(double terrainElev) +void FGPropagate::SetSeaLevelRadius(double tt) { - LocalTerrainRadius = terrainElev + SeaLevelRadius; - FDMExec->GetGroundCallback()->SetTerrainGeoCentRadius(LocalTerrainRadius); + FDMExec->GetGroundCallback()->SetSeaLevelRadius(tt); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -double FGPropagate::GetTerrainElevation(void) const +double FGPropagate::GetLocalTerrainRadius(void) const { - return FDMExec->GetGroundCallback()->GetTerrainGeoCentRadius()-SeaLevelRadius; + return VState.vLocation.GetTerrainRadius(FDMExec->GetSimTime()); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -const FGMatrix33& FGPropagate::GetTi2ec(void) +double FGPropagate::GetDistanceAGL(void) const { - return VState.vLocation.GetTi2ec(Inertial->GetEarthPositionAngle()); + return VState.vLocation.GetAltitudeAGL(FDMExec->GetSimTime()); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -const FGMatrix33& FGPropagate::GetTec2i(void) +void FGPropagate::SetDistanceAGL(double tt) { - return VState.vLocation.GetTec2i(Inertial->GetEarthPositionAngle()); + VState.vLocation.SetAltitudeAGL(tt, FDMExec->GetSimTime()); + UpdateVehicleState(); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -void FGPropagate::SetAltitudeASL(double altASL) +void FGPropagate::SetVState(const VehicleState& vstate) { - VState.vLocation.SetRadius( altASL + SeaLevelRadius ); + //ToDo: Shouldn't all of these be set from the vstate vector passed in? + VState.vLocation = vstate.vLocation; + Ti2ec = VState.vLocation.GetTi2ec(); // useless ? + Tec2i = Ti2ec.Transposed(); + UpdateLocationMatrices(); + SetInertialOrientation(vstate.qAttitudeECI); + RecomputeLocalTerrainVelocity(); + VehicleRadius = GetRadius(); + VState.vUVW = vstate.vUVW; + vVel = Tb2l * VState.vUVW; + VState.vPQR = vstate.vPQR; + VState.vPQRi = VState.vPQR + Ti2b * in.vOmegaPlanet; + VState.vInertialPosition = vstate.vInertialPosition; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -double FGPropagate::GetLocalTerrainRadius(void) const +void FGPropagate::UpdateVehicleState(void) { - return LocalTerrainRadius; + RecomputeLocalTerrainVelocity(); + VehicleRadius = GetRadius(); + VState.vInertialPosition = Tec2i * VState.vLocation; + UpdateLocationMatrices(); + UpdateBodyMatrices(); + vVel = Tb2l * VState.vUVW; + VState.qAttitudeLocal = Tl2b.GetQuaternion(); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -double FGPropagate::GetDistanceAGL(void) const +void FGPropagate::SetLocation(const FGLocation& l) { - return VState.vLocation.GetRadius() - LocalTerrainRadius; + VState.vLocation = l; + Ti2ec = VState.vLocation.GetTi2ec(); // useless ? + Tec2i = Ti2ec.Transposed(); + UpdateVehicleState(); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -void FGPropagate::SetDistanceAGL(double tt) +void FGPropagate::DumpState(void) { - VState.vLocation.SetRadius( tt + LocalTerrainRadius ); + cout << endl; + cout << fgblue + << "------------------------------------------------------------------" << reset << endl; + cout << highint + << "State Report at sim time: " << FDMExec->GetSimTime() << " seconds" << reset << endl; + cout << " " << underon + << "Position" << underoff << endl; + cout << " ECI: " << VState.vInertialPosition.Dump(", ") << " (x,y,z, in ft)" << endl; + cout << " ECEF: " << VState.vLocation << " (x,y,z, in ft)" << endl; + cout << " Local: " << VState.vLocation.GetLatitudeDeg() + << ", " << VState.vLocation.GetLongitudeDeg() + << ", " << GetAltitudeASL() << " (lat, lon, alt in deg and ft)" << endl; + + cout << endl << " " << underon + << "Orientation" << underoff << endl; + cout << " ECI: " << VState.qAttitudeECI.GetEulerDeg().Dump(", ") << " (phi, theta, psi in deg)" << endl; + cout << " Local: " << VState.qAttitudeLocal.GetEulerDeg().Dump(", ") << " (phi, theta, psi in deg)" << endl; + + cout << endl << " " << underon + << "Velocity" << underoff << endl; + cout << " ECI: " << VState.vInertialVelocity.Dump(", ") << " (x,y,z in ft/s)" << endl; + cout << " ECEF: " << (Tb2ec * VState.vUVW).Dump(", ") << " (x,y,z in ft/s)" << endl; + cout << " Local: " << GetVel() << " (n,e,d in ft/sec)" << endl; + cout << " Body: " << GetUVW() << " (u,v,w in ft/sec)" << endl; + + cout << endl << " " << underon + << "Body Rates (relative to given frame, expressed in body frame)" << underoff << endl; + cout << " ECI: " << (VState.vPQRi*radtodeg).Dump(", ") << " (p,q,r in deg/s)" << endl; + cout << " ECEF: " << (VState.vPQR*radtodeg).Dump(", ") << " (p,q,r in deg/s)" << endl; } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -518,7 +598,7 @@ void FGPropagate::SetDistanceAGL(double tt) void FGPropagate::bind(void) { typedef double (FGPropagate::*PMF)(int) const; -// typedef double (FGPropagate::*dPMF)() const; + PropertyManager->Tie("velocities/h-dot-fps", this, &FGPropagate::Gethdot); PropertyManager->Tie("velocities/v-north-fps", this, eNorth, (PMF)&FGPropagate::GetVel); @@ -539,20 +619,12 @@ void FGPropagate::bind(void) PropertyManager->Tie("velocities/eci-velocity-mag-fps", this, &FGPropagate::GetInertialVelocityMagnitude); - PropertyManager->Tie("accelerations/pdot-rad_sec2", this, eP, (PMF)&FGPropagate::GetPQRdot); - PropertyManager->Tie("accelerations/qdot-rad_sec2", this, eQ, (PMF)&FGPropagate::GetPQRdot); - PropertyManager->Tie("accelerations/rdot-rad_sec2", this, eR, (PMF)&FGPropagate::GetPQRdot); - - PropertyManager->Tie("accelerations/udot-ft_sec2", this, eU, (PMF)&FGPropagate::GetUVWdot); - PropertyManager->Tie("accelerations/vdot-ft_sec2", this, eV, (PMF)&FGPropagate::GetUVWdot); - PropertyManager->Tie("accelerations/wdot-ft_sec2", this, eW, (PMF)&FGPropagate::GetUVWdot); - PropertyManager->Tie("position/h-sl-ft", this, &FGPropagate::GetAltitudeASL, &FGPropagate::SetAltitudeASL, true); PropertyManager->Tie("position/h-sl-meters", this, &FGPropagate::GetAltitudeASLmeters, &FGPropagate::SetAltitudeASLmeters, true); - PropertyManager->Tie("position/lat-gc-rad", this, &FGPropagate::GetLatitude, &FGPropagate::SetLatitude); - PropertyManager->Tie("position/long-gc-rad", this, &FGPropagate::GetLongitude, &FGPropagate::SetLongitude); - PropertyManager->Tie("position/lat-gc-deg", this, &FGPropagate::GetLatitudeDeg, &FGPropagate::SetLatitudeDeg); - PropertyManager->Tie("position/long-gc-deg", this, &FGPropagate::GetLongitudeDeg, &FGPropagate::SetLongitudeDeg); + PropertyManager->Tie("position/lat-gc-rad", this, &FGPropagate::GetLatitude, &FGPropagate::SetLatitude, false); + PropertyManager->Tie("position/long-gc-rad", this, &FGPropagate::GetLongitude, &FGPropagate::SetLongitude, false); + PropertyManager->Tie("position/lat-gc-deg", this, &FGPropagate::GetLatitudeDeg, &FGPropagate::SetLatitudeDeg, false); + PropertyManager->Tie("position/long-gc-deg", this, &FGPropagate::GetLongitudeDeg, &FGPropagate::SetLongitudeDeg, false); PropertyManager->Tie("position/lat-geod-rad", this, &FGPropagate::GetGeodLatitudeRad); PropertyManager->Tie("position/lat-geod-deg", this, &FGPropagate::GetGeodLatitudeDeg); PropertyManager->Tie("position/geod-alt-ft", this, &FGPropagate::GetGeodeticAltitude); @@ -562,6 +634,7 @@ void FGPropagate::bind(void) &FGPropagate::GetTerrainElevation, &FGPropagate::SetTerrainElevation, false); + PropertyManager->Tie("position/epa-rad", this, &FGPropagate::GetEarthPositionAngle); PropertyManager->Tie("metrics/terrain-radius", this, &FGPropagate::GetLocalTerrainRadius); PropertyManager->Tie("attitude/phi-rad", this, (int)ePhi, (PMF)&FGPropagate::GetEuler); @@ -571,11 +644,11 @@ void FGPropagate::bind(void) PropertyManager->Tie("attitude/roll-rad", this, (int)ePhi, (PMF)&FGPropagate::GetEuler); PropertyManager->Tie("attitude/pitch-rad", this, (int)eTht, (PMF)&FGPropagate::GetEuler); PropertyManager->Tie("attitude/heading-true-rad", this, (int)ePsi, (PMF)&FGPropagate::GetEuler); - - PropertyManager->Tie("simulation/integrator/rate/rotational", &integrator_rotational_rate); - PropertyManager->Tie("simulation/integrator/rate/translational", &integrator_translational_rate); - PropertyManager->Tie("simulation/integrator/position/rotational", &integrator_rotational_position); - PropertyManager->Tie("simulation/integrator/position/translational", &integrator_translational_position); + + PropertyManager->Tie("simulation/integrator/rate/rotational", (int*)&integrator_rotational_rate); + PropertyManager->Tie("simulation/integrator/rate/translational", (int*)&integrator_translational_rate); + PropertyManager->Tie("simulation/integrator/position/rotational", (int*)&integrator_rotational_position); + PropertyManager->Tie("simulation/integrator/position/translational", (int*)&integrator_translational_position); } //%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -612,7 +685,96 @@ void FGPropagate::Debug(int from) } if (debug_lvl & 4 ) { // Run() method entry print for FGModel-derived objects } - if (debug_lvl & 8 ) { // Runtime state variables + if (debug_lvl & 8 && from == 2) { // Runtime state variables + cout << endl << fgblue << highint << left + << " Propagation Report (English units: ft, degrees) at simulation time " << FDMExec->GetSimTime() << " seconds" + << reset << endl; + cout << endl; + cout << highint << " Earth Position Angle (deg): " << setw(8) << setprecision(3) << reset + << GetEarthPositionAngleDeg() << endl; + cout << endl; + cout << highint << " Body velocity (ft/sec): " << setw(8) << setprecision(3) << reset << VState.vUVW << endl; + cout << highint << " Local velocity (ft/sec): " << setw(8) << setprecision(3) << reset << vVel << endl; + cout << highint << " Inertial velocity (ft/sec): " << setw(8) << setprecision(3) << reset << VState.vInertialVelocity << endl; + cout << highint << " Inertial Position (ft): " << setw(10) << setprecision(3) << reset << VState.vInertialPosition << endl; + cout << highint << " Latitude (deg): " << setw(8) << setprecision(3) << reset << VState.vLocation.GetLatitudeDeg() << endl; + cout << highint << " Longitude (deg): " << setw(8) << setprecision(3) << reset << VState.vLocation.GetLongitudeDeg() << endl; + cout << highint << " Altitude ASL (ft): " << setw(8) << setprecision(3) << reset << GetAltitudeASL() << endl; +// cout << highint << " Acceleration (NED, ft/sec^2): " << setw(8) << setprecision(3) << reset << Tb2l*GetUVWdot() << endl; + cout << endl; + cout << highint << " Matrix ECEF to Body (Orientation of Body with respect to ECEF): " + << reset << endl << Tec2b.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tec2b.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Body to ECEF (Orientation of ECEF with respect to Body):" + << reset << endl << Tb2ec.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tb2ec.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Local to Body (Orientation of Body with respect to Local):" + << reset << endl << Tl2b.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tl2b.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Body to Local (Orientation of Local with respect to Body):" + << reset << endl << Tb2l.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tb2l.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Local to ECEF (Orientation of ECEF with respect to Local):" + << reset << endl << Tl2ec.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tl2ec.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix ECEF to Local (Orientation of Local with respect to ECEF):" + << reset << endl << Tec2l.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tec2l.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix ECEF to Inertial (Orientation of Inertial with respect to ECEF):" + << reset << endl << Tec2i.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tec2i.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Inertial to ECEF (Orientation of ECEF with respect to Inertial):" + << reset << endl << Ti2ec.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Ti2ec.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Inertial to Body (Orientation of Body with respect to Inertial):" + << reset << endl << Ti2b.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Ti2b.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Body to Inertial (Orientation of Inertial with respect to Body):" + << reset << endl << Tb2i.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tb2i.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Inertial to Local (Orientation of Local with respect to Inertial):" + << reset << endl << Ti2l.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Ti2l.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << highint << " Matrix Local to Inertial (Orientation of Inertial with respect to Local):" + << reset << endl << Tl2i.Dump("\t", " ") << endl; + cout << highint << " Associated Euler angles (deg): " << setw(8) + << setprecision(3) << reset << (Tl2i.GetQuaternion().GetEuler()*radtodeg) + << endl << endl; + + cout << setprecision(6); // reset the output stream } if (debug_lvl & 16) { // Sanity checking if (from == 2) { // State sanity checking