private void Start()
{
var g = 9.81;
var k = 0.000007757;
var m = 0.00007;
_numericalSimulation = GetSimulation();
_numericalSimulation.Setup(0.0, 0.0, _epsilon);
_numericalSimulation.SetupYDot(f_y_t: (double y, double t) => (g - k / m * y * y));
}
private void Start()
{
// get initial state
var initialTheta1 = _doublePendulum.Theta_1;
var initialTheta2 = _doublePendulum.Theta_2;
_l_1 = _doublePendulum.Link1Length;
_l_2 = _doublePendulum.Link2Length;
_m_1 = _doublePendulum.Mass1;
_m_2 = _doublePendulum.Mass2;
_NumericalSimLambda1 = GetNumericalSimulator();
_NumericalSimLambda1.Setup(t_0: 0.0, y_0: 0.0, epsilon: _epsilon);
_NumericalSimuLambda2 = GetNumericalSimulator();
_NumericalSimuLambda2.Setup(t_0: 0.0, y_0: 0.0, epsilon: _epsilon);
_NumericalSimTheta1 = GetNumericalSimulator();
_NumericalSimTheta1.Setup(t_0: 0.0, y_0: initialTheta1, epsilon: _epsilon);
_NumericalSimTheta2 = GetNumericalSimulator();
_NumericalSimTheta2.Setup(t_0: 0.0, y_0: initialTheta2, epsilon: _epsilon);
// eq:9
/*
* \dot{\lambda}_1 =
* \frac
* {
* - m_2 l_2 \dot{\lambda}_2 \cos(\theta_1 - \theta_2)
* - m_2 l_2 \lambda^2_2 \sin(\theta_1 - \theta_2)
* - g (m_1 + m_2) \sin \theta_1
* }
* {
* (m_1 + m_2) l_1
* }
*/
_NumericalSimLambda1.SetupYDot((double lambda1, double t) =>
(-_m_2 * _l_2 * _NumericalSimuLambda2.Current_y_dot *
Math.Cos(_NumericalSimTheta1.Current_y - _NumericalSimTheta2.Current_y)
- _m_2 * _l_2 * _NumericalSimuLambda2.Current_y * _NumericalSimuLambda2.Current_y *
Math.Sin(_NumericalSimTheta1.Current_y - _NumericalSimTheta2.Current_y)
- _g * (_m_1 + _m_2) * Math.Sin(_NumericalSimTheta1.Current_y))
/
((_m_1 + _m_2) * _l_1));
// label{eq:10}
// \dot{\theta}_1 = \lambda_1
_NumericalSimTheta1.SetupYDot((double theta1, double t) => _NumericalSimLambda1.Current_y);
// eq:11
/*
* \dot{\lambda}_2 =
* \frac
* {
* m_2 l_1 \lambda^2_1 sin(\theta_1 - \theta_2)
* - m_2 l_1 \dot{\lambda}_1 cos(\theta_1 - \theta_2)
* - m_2 g \sin \theta_2
* }
* {
* m_2 l_2
* }
*
*/
_NumericalSimuLambda2.SetupYDot((double lambda2, double t) =>
(_m_2 * _l_1 * _NumericalSimLambda1.Current_y * _NumericalSimLambda1.Current_y *
Math.Sin(_NumericalSimTheta1.Current_y - _NumericalSimTheta2.Current_y)
- _m_2 * _l_1 * _NumericalSimLambda1.Current_y_dot *
Math.Cos(_NumericalSimTheta1.Current_y - _NumericalSimTheta2.Current_y)
- _m_2 * _g * Math.Sin(_NumericalSimTheta2.Current_y))
/
(_m_2 * _l_2));
// no label (not written about this one yet)
// \dot{\theta}_2 = \lambda_2
_NumericalSimTheta2.SetupYDot((double theta2, double t) => _NumericalSimuLambda2.Current_y);
}
private void Start()
{
_numericalSimulation = GetSimulation();
_numericalSimulation.Setup(0.0, 0.5, _epsilon);
_numericalSimulation.SetupYDot(f_y_t: (double y, double t) => 2 * y / (1 + t));
}