//----------------------------------------------------------------------------- // File: RotatingBook.cpp // Class: None // Parent: None // Children: None // Purpose: Simulates rotating motion of a book //----------------------------------------------------------------------------- // The following are standard C/C++ header files. // If a filename is enclosed inside < > it means the header file is in the Include directory. // If a filename is enclosed inside " " it means the header file is in the current directory. #include // Character Types #include // Mathematical Constants #include // Variable Argument Lists #include // Standard Input/Output Functions #include // Utility Functions #include // String Operations #include // Signals (Contol-C + Unix System Calls) #include // Nonlocal Goto (For Control-C) #include // Time and Date information #include // Verify Program Assertion #include // Error Codes (Used in Unix system()) #include // Floating Point Constants #include // Implementation Constants #include // Standard Definitions #include // Exception handling (e.g., try, catch throw) //----------------------------------------------------------------------------- #include "SimTKsimbody.h" using namespace SimTK; using namespace std; //----------------------------------------------------------------------------- #define PI 3.141592653589793238462643 //----------------------------------------------------------------------------- // Prototypes for local functions (functions not called by code in other files) //----------------------------------------------------------------------------- bool SimulateRotatingBook( void ); bool WriteStringToFile( const char outputString[], FILE *fptr ) { return fputs( outputString, fptr ) != 0; } bool WriteStringToScreen( const char outputString[] ) { return WriteStringToFile( outputString, stdout ); } bool WriteDoubleToFile( double x, int precision, FILE *fptr ); FILE* FileOpenWithMessageIfCannotOpen( const char *filename, const char *attribute ); //----------------------------------------------------------------------------- // The executable program starts here //----------------------------------------------------------------------------- int main( int numberOfCommandLineArguments, char *arrayOfCommandLineArguments[] ) { // Simulate the multibody system bool simulationSucceeded = SimulateRotatingBook(); // Keep the screen displayed until the user presses the Enter key WriteStringToScreen( "\n\n Press Enter to terminate the program: " ); getchar(); // The value returned by the main function is the exit status of the program. // A normal program exit returns 0 (other return values usually signal an error). return simulationSucceeded == true ? 0 : 1; } //----------------------------------------------------------------------------- bool SimulateRotatingBook( void ) { // Declare a multibody system (contains one or more force and matter sub-systems) MultibodySystem mbs; // 0. The ground's right-handed, orthogonal x,y,z unit vectors are directed with x horizontally right and y vertically upward. // 1. Create a gravity vector that is straight down (in the ground's frame) // 2. Create a uniform gravity sub-system // 3. Add the gravity sub-system to the multibody system Vec3 gravityVector( 0, -9.8, 0 ); UniformGravitySubsystem gravity( gravityVector ); mbs.addForceSubsystem( gravity ); // Create a matter sub-system (the book) SimbodyMatterSubsystem book; // Create the mass, center of mass, and inertia properties for the book const Real massOfBook = 0.4; // The location of the book's center of mass is a vector from the book's // origin expressed in the "x, y, z"' unit vectors fixed in the book's frame. // Example: The vector(0,0,0) locates the book's center of mass at the book's origin. // Example: The vector(1,0,0) locates the book's center of mass 1 unit in the "x" direction from the book's origin. const Vec3 bookCenterOfMassLocation( 0, 0, 0 ); // Create the book's inertia matrix about its origin for the "x, y, z" unit vectors fixed in the book's frame. // Note: The 3x3 inertia matrix is symmetric - so only 6 elements need to be defined. // Ixx, Iyy, Izz are moments of inertia ( diagonal terms in the matrix) // Ixy, Ixz, Iyz are products of inertia (off-diagonal terms in the matrix) const Real a = 0.05, b = 0.30, c = 0.20; const Real Ixx = 1/12.0*massOfBook*(a*a+b*b), Iyy = 1/12.0*massOfBook*(a*a+c*c), Izz = 1/12.0*massOfBook*(c*c+b*b); const Real Ixy = 0, Ixz = 0, Iyz = 0; const Inertia bookInertiaMatrix( Ixx, Iyy, Izz, Ixy, Ixz, Iyz ); // The MassProperties class holds the mass, center of mass, and inertia properties of a rigid body. // Although the next line creates an instance of the MassProperties class for the book, // it does not get associated with the book until the addRigidBody method. MassProperties bookMassProperties( massOfBook, bookCenterOfMassLocation, bookInertiaMatrix ); // The motion of the book is related to the motion of the ground via "mobilizers" // The "mobilizers" specify the allowable motion of the book to the ground. // More specifically, the motion of an "outboard body" (e.g., the book) // to its inboard body (e.g., the ground) is specified by first constructing: // 1. An "outboard frame" on the ground (which hooks to the "outboard body" - the book ) // 2. An "inboard frame" on the book (which hooks to the "inboard body" - the ground) // The orientation and position of the outboard frame from the ground's frame is specified below. // The outboard frame's axes are aligned with the ground's axes and its origin is coincident with the ground's origin. // In other words, for this simple problem the outboard frame and the ground frame are identical. const Transform outboardFrameTransformFromGround; // The default constructor is the identity transform // The orientation and position of the inboard frame from the book's frame is specified below. // The inboard frame's axes are aligned with the book's axes and its origin is coincident with the book's origin // In other words, for this simple problem the inboard frame and the book frame are identical. // Although the inboard frame can be constructed in a simple manner analogous to the outboardFrameTransformFromGround (above) // it is worthwhile to look at the details of the rotation matrix and position vector in the transform: // a. The rotation matrix relating the InboardFrame's x,y,z axes to the bookFrame's x,y,z axes is specified InboardFrame_BookFrame. // b. The position of the InboardFrame's origin from the BookFrame origin, expressed in terms of the BookFrame's "x, y, z" unit vectors. const Rotation inboardFrameOrientationInBook; // ( 1,0,0, 0,1,0, 0,0,1 ); const Vec3 inboardFrameOriginLocationFromBookOrigin( 0, 0, 0 ); const Transform inboardFrameTransformFromBook( inboardFrameOrientationInBook, inboardFrameOriginLocationFromBookOrigin ); // There are many ways that the book can move relative to the ground. // The following allows the book to move in "x", "y", and "z" directions. // Another option producing the same result is Mobilizer::Free Mobilizer bookToGroundMobilizer = Mobilizer::Ball; const BodyId bookBodyId = book.addRigidBody( bookMassProperties, inboardFrameTransformFromBook, GroundId, outboardFrameTransformFromGround, bookToGroundMobilizer ); // Add the matter (book) sub-system to the system. mbs.setMatterSubsystem( book ); // Create a state for this system. // Define appropriate states for this multi-body system. // Set the initial time to 0.0 State s; mbs.realize( s ); s.setTime( 0.0 ); // Set the initial values for the configuration variables (x,y,z) book.setMobilizerQ( s, bookBodyId, 0, 1.0 ); book.setMobilizerQ( s, bookBodyId, 1, 0.0 ); book.setMobilizerQ( s, bookBodyId, 2, 0.0 ); book.setMobilizerQ( s, bookBodyId, 3, 0.0 ); // Set the initial values for the motion variables //const Real wx = 0.2, wy = 7.0, wz = 0.2; // Spin about minimum axis //const Real wx = 7.0, wy = 0.2, wz = 0.2; // Spin about intermediate axis const Real wx = 0.2, wy = 0.2, wz = 7.0; // Spin about maximum axis book.setMobilizerU( s, bookBodyId, 0, wx ); book.setMobilizerU( s, bookBodyId, 1, wy ); book.setMobilizerU( s, bookBodyId, 2, wz ); // Create a study using the Runge Kutta Merson integrator (alternately use the CPodesIntegrator) RungeKuttaMerson myStudy( mbs, s ); // Set the numerical accuracy for the integrator myStudy.setAccuracy( 1.0E-7 ); // The next statement does lots of accounting myStudy.initialize(); // Open a file to record the simulation results (they are also displayed on screen) FILE *outputFile = FileOpenWithMessageIfCannotOpen( "RotatingBookResults.txt", "w" ); WriteStringToFile( " time wx wy wz Hx Hy Hz magH K\n", outputFile ); WriteStringToScreen( " time wx wy wz Hx Hy Hz magH K\n" ); // Visualize results with VTKReporter VTKReporter animationResults( mbs ); // For visualization purposes only, create a red brick with a radius of 0.5 meters (huge but visible) const Vec3 halfLengths( c/2.0, b/2.0, a/2.0 ); DecorativeBrick redBrick = DecorativeBrick( halfLengths ); redBrick.setColor(Red); // Can also specify a Vec3 with rgb which scale from 0 to 1 redBrick.setOpacity(0.0); // 0.0 is solid and 1.0 is transparent // Decorate the book with the red brick at the book's origin const Rotation bookToRedBrickOrientation; //( 1,0,0, 0,1,0, 0,0,1 ); const Vec3 bookOriginToRedBrickOriginLocation( 0, 0, 0 ); const Transform bookToRedBrickTransform( bookToRedBrickOrientation, bookOriginToRedBrickOriginLocation ); animationResults.addDecoration( bookBodyId, bookToRedBrickTransform, redBrick ); // Set the numerical integration step and the time for the simulation to run const Real dt = 0.01; const Real finalTime = 4.0; // Run the simulation and print the results while( 1 ) { // Query for results to be printed Real time = s.getTime(); Real kineticEnergy = mbs.getKineticEnergy(s); Real uniformGravitationalPotentialEnergy = mbs.getPotentialEnergy(s); Real mechanicalEnergy = kineticEnergy + uniformGravitationalPotentialEnergy; // Locate the book origin's from the ground's origin, expressed in terms of the ground's "x,y,z" unit vectors. // Extract the book's y-location from this vector. const Vec3 bookLocation = book.calcBodyOriginLocationInBody( s, bookBodyId, GroundId ); Real xLoc = bookLocation[0]; Real yLoc = bookLocation[1]; Real zLoc = bookLocation[2]; // Get the book origin's velocity in ground, expressed in terms of the ground's "x,y,z" unit vectors. // Extract the book's y-velocity from this vector. const Vec3 bookVelocity = book.calcBodyOriginVelocityInBody( s, bookBodyId, GroundId ); Real xLinVelocity = bookVelocity[0]; Real yLinVelocity = bookVelocity[1]; Real zLinVelocity = bookVelocity[2]; const Vec3 bookAngularVelocityExpressedInGround = book.calcBodyAngularVelocityInBody( s, bookBodyId, GroundId ); Real xAngVelocity = bookAngularVelocityExpressedInGround[0]; Real yAngVelocity = bookAngularVelocityExpressedInGround[1]; Real zAngVelocity = bookAngularVelocityExpressedInGround[2]; // Get rotation matrix from ground to book & invert Rotation rotationFromGroundToBook = book.getBodyRotation( s, bookBodyId ); Rotation rotationFromBookToGround = rotationFromGroundToBook.invert(); Vec3 angularVelocityExpressedInBook = rotationFromBookToGround*bookAngularVelocityExpressedInGround; Real angVelX = angularVelocityExpressedInBook[0]; Real angVelY = angularVelocityExpressedInBook[1]; Real angVelZ = angularVelocityExpressedInBook[2]; // Find angular momentum of book about its center of mass. const SpatialVec H_CB = book.calcBodyMomentumAboutBodyMassCenterInGround( s, bookBodyId); Real H_CB_x = Ixx*angVelX; Real H_CB_y = Iyy*angVelY; Real H_CB_z = Izz*angVelZ; Real magH = sqrt( H_CB_x*H_CB_x + H_CB_y*H_CB_y + H_CB_z*H_CB_z ); // Print results to screen WriteDoubleToFile( time, 2, stdout ); WriteDoubleToFile( angVelX, 4, stdout ); WriteDoubleToFile( angVelY, 4, stdout ); WriteDoubleToFile( angVelZ, 4, stdout ); WriteDoubleToFile( H_CB_x, 4, stdout ); WriteDoubleToFile( H_CB_y, 4, stdout ); WriteDoubleToFile( H_CB_z, 4, stdout ); WriteDoubleToFile( magH, 4, stdout ); WriteDoubleToFile( kineticEnergy, 7, stdout ); WriteStringToScreen( "\n" ); // Print results to file WriteDoubleToFile( time, 2, outputFile ); WriteDoubleToFile( angVelX, 4, outputFile ); WriteDoubleToFile( angVelY, 4, outputFile ); WriteDoubleToFile( angVelZ, 4, outputFile ); WriteDoubleToFile( H_CB_x, 4, outputFile ); WriteDoubleToFile( H_CB_y, 4, outputFile ); WriteDoubleToFile( H_CB_z, 4, outputFile ); WriteDoubleToFile( magH, 4, outputFile ); WriteDoubleToFile( kineticEnergy, 7, outputFile ); WriteStringToFile( "\n", outputFile ); // Animate the results for this step animationResults.report(s); // Check if integration has completed if( time >= finalTime ) break; // Increment time step myStudy.step( time + dt); } // Simulation completed properly return true; } //----------------------------------------------------------------------------- FILE* FileOpenWithMessageIfCannotOpen( const char *filename, const char *attribute ) { // Try to open the file FILE *Fptr1 = fopen( filename, attribute ); // If unable to open the file, issue a message if( !Fptr1 ) { WriteStringToScreen( "\n\n Unable to open the file: " ); WriteStringToScreen( filename ); WriteStringToScreen( "\n\n" ); } return Fptr1; } //----------------------------------------------------------------------------- bool WriteDoubleToFile( double x, int precision, FILE *fptr ) { // Ensure the precision (number of digits in the mantissa after the decimal point) makes sense. // Next, calculate the field width so it includes one extra space to the right of the number. if( precision < 0 || precision > 17 ) precision = 5; int fieldWidth = precision + 8; // Create the format specifier and print the number char format[20]; sprintf( format, " %%- %d.%dE", fieldWidth, precision ); return fprintf( fptr, format, x ) >= 0; }