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/*
* Copyright (C) 2018 Open Source Robotics Foundation
*
* 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.
*
*/
#include <cmath>
#include <ignition/plugin/Register.hh>
#include "integrators.hh"
namespace ignition {
namespace plugin {
namespace examples {
namespace ExponentialODE {
/// \brief Create an exponential ODE, like radioactive decay or continuously
/// compounding interest.
ODESystem CreateExponentialODE(
const double t0 = 0.0,
const double x0 = 1.0,
const double base = std::exp(1),
const double lambda = 1.0)
{
ODESystem exponential;
exponential.name = "exponential ode";
exponential.initialTime = t0;
exponential.exact = [=](const NumericalIntegrator::Time _t)
-> NumericalIntegrator::State
{
return { x0 * std::pow(base, lambda*_t) };
};
exponential.initialState = exponential.exact(t0);
exponential.ode = [=](const NumericalIntegrator::Time /*_t*/,
const NumericalIntegrator::State &_state)
-> NumericalIntegrator::State
{
const double ln_base = std::log(base);
return { x0*lambda * std::pow(_state[0], lambda/ln_base) * ln_base };
};
return exponential;
}
/// \brief Create an ODE system that represents a circular trajectory.
ODESystem CreateCircularSystem(
const double t0 = 0.0,
const double theta0 = 0.0,
const double R = 1.0,
const double w = 1.0)
{
ODESystem circular;
circular.name = "circular system";
circular.initialTime = t0;
circular.exact = [=](const NumericalIntegrator::Time _t)
-> NumericalIntegrator::State
{
return { R * cos(w * (_t-t0) + theta0), R * sin(w * (_t-t0) + theta0) };
};
circular.initialState = circular.exact(t0);
circular.ode = [=](const NumericalIntegrator::Time _t,
const NumericalIntegrator::State &_state)
-> NumericalIntegrator::State
{
return { -w * _state[1], w * _state[0] };
};
return circular;
}
/// \brief Create an ODE system that represents an exponential spiral trajectory
ODESystem CreateSpiralSystem(
const double t0 = 0.0,
const double theta0 = 0.0,
const double R0 = 0.1,
const double lambda = 0.5,
const double w = 1.0)
{
ODESystem spiral;
spiral.name = "exponential spiral system";
spiral.initialTime = t0;
spiral.exact = [=](const NumericalIntegrator::Time _t)
-> NumericalIntegrator::State
{
return {
R0 * std::exp(lambda*(_t-t0)) * cos(w*(_t-t0) + theta0),
R0 * std::exp(lambda*(_t-t0)) * cos(w*(_t-t0) + theta0)
};
};
spiral.initialState = spiral.exact(t0);
spiral.ode = [=](const NumericalIntegrator::Time /*_t*/,
const NumericalIntegrator::State &_state)
-> NumericalIntegrator::State
{
return { lambda * _state[0] - w * _state[1],
lambda * _state[1] + w * _state[0] };
};
return spiral;
}
/// \brief A factory that provides these exponential ODE systems
class Factory : public ODESystemFactory
{
public: std::vector<ODESystem> CreateSystems() override
{
return {
CreateExponentialODE(),
CreateCircularSystem(),
CreateSpiralSystem()
};
}
};
IGNITION_ADD_PLUGIN(Factory, ODESystemFactory)
}
}
}
}
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