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/* -------------------------------------------------------------------------- *
* Simbody(tm) Example: Dzhanibekov Effect *
* -------------------------------------------------------------------------- *
* This is part of the SimTK biosimulation toolkit originating from *
* Simbios, the NIH National Center for Physics-Based Simulation of *
* Biological Structures at Stanford, funded under the NIH Roadmap for *
* Medical Research, grant U54 GM072970. See https://simtk.org/home/simbody. *
* *
* Portions copyright (c) 2015 Stanford University and the Authors. *
* Authors: Michael Sherman *
* Contributors: *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); you may *
* not use this file except in compliance with the License. You may obtain a *
* copy of the License at http://www.apache.org/licenses/LICENSE-2.0. *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* -------------------------------------------------------------------------- */
/* Simbody Dzhanibekov Effect
This example demonstrates a non-intuitive behavior of a freely rotating
rigid body, known as the Dzhanibekov Effect. This is best seen in zero
gravity on the space station. Here are some cool real-world videos:
https://www.youtube.com/watch?v=L2o9eBl_Gzw
https://www.youtube.com/watch?v=JB0OAt4zQ1E
And here is one generated from this example:
https://youtu.be/L8B83DUKiiA
*/
#include "Simbody.h"
#include <iostream>
using namespace SimTK;
//==============================================================================
// SHOW ENERGY
//==============================================================================
// Generate text in the scene that displays the total energy, which should be
// conserved to roughly the number of decimal places corresponding to the
// accuracy setting (i.e., acc=1e-5 -> 5 digits).
class ShowEnergy : public DecorationGenerator {
public:
explicit ShowEnergy(const MultibodySystem& mbs) : m_mbs(mbs) {}
void generateDecorations(const State& state,
Array_<DecorativeGeometry>& geometry) override;
private:
const MultibodySystem& m_mbs;
};
//==============================================================================
// MAIN
//==============================================================================
int main() {
try {
// Create the system.
MultibodySystem system; system.setUpDirection(ZAxis);
SimbodyMatterSubsystem matter(system);
// No gravity or other forces
matter.setShowDefaultGeometry(false); // turn off frames and other junk
// Construct a single rigid body by welding together a cylindrical shaft
// and a rectangular bar.
Rotation YtoX(-Pi/2, ZAxis);
Body::Rigid shaftBody(MassProperties(1, Vec3(0),
UnitInertia::cylinderAlongX(.02, .05)));
shaftBody.addDecoration(YtoX,
DecorativeCylinder(.02, .05).setColor(Red));
const Vec3 halfLengths(.02,.04,.3);
Body::Rigid barBody(MassProperties(2, Vec3(0),
UnitInertia::brick(halfLengths)));
barBody.addDecoration(Transform(),
DecorativeBrick(halfLengths).setColor(Blue));
MobilizedBody::Free shaft(matter.Ground(), Transform(),
shaftBody, Transform());
MobilizedBody::Weld bar(shaft, Vec3(-.05,0,0),
barBody, Vec3(halfLengths[0],0,0));
// Visualize a frame every 1/60 s, and include the energy.
Visualizer viz(system); viz.setDesiredFrameRate(60);
viz.addDecorationGenerator(new ShowEnergy(system));
system.addEventReporter(new Visualizer::Reporter(viz, 1./60));
// Initialize the system and state.
State state = system.realizeTopology();
// Set initial conditions. Need a slight perturbation of angular velocity
// to trigger the instability.
shaft.setQToFitTranslation(state, Vec3(0,0,.5));
shaft.setUToFitAngularVelocity(state, Vec3(10,0,1e-10)); // 10 rad/s
// Simulate it.
RungeKuttaMersonIntegrator integ(system);
integ.setAccuracy(1e-5);
TimeStepper ts(system, integ);
ts.initialize(state);
ts.stepTo(100.0);
} catch(const std::exception& e) {
std::cout << "EXCEPTION: " << e.what() << std::endl;
return 1;
}
return 0;
}
void ShowEnergy::generateDecorations(const State& state,
Array_<DecorativeGeometry>& geometry)
{
m_mbs.realize(state, Stage::Dynamics);
const Real E=m_mbs.calcEnergy(state);
DecorativeText energy;
energy.setTransform(Vec3(-.2,0,.5))
.setText("Energy: " + String(E, "%.6f"))
.setScale(.09)
.setColor(Black);
geometry.push_back(energy);
}
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