// a single Leapfrog step (parameter = step length)
void Solvers::Leapfrog(double step)
{
int n = this->_leapfrog->n(); // number of celestial bodies
double halfStep = (step / 2.0);
// calculate forces/accelerations based on current postions
this->_leapfrog->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_leapfrog->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// Leapfrog algorithm, step 1
*(cb->velocity) += halfStep * cb->acc();
// Leapfrog algorithm, step 2
*(cb->position) += step * *(cb->velocity);
}
}
// calculate the forces using the new positions
this->_leapfrog->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_leapfrog->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// Leapfrog algorithm, step 3
*(cb->velocity) += halfStep * cb->acc();
}
}
}
// a single Euler-Cromer step (parameter = step length)
void Solvers::Euler(double step)
{
int n = this->_euler->n(); // number of celestial bodies
// calculate forces/accelerations based on current postions
this->_euler->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_euler->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// acc -> velocity (Euler-Cromer, for testing only)
*(cb->velocity) += step * cb->acc();
// velocity -> position (Euler-Cromer, for testing only)
*(cb->position) += step * *(cb->velocity);
}
}
}
// a single Runge-Kutta step (parameter = step length)
void Solvers::RK4(double step)
{
int n = this->_rk4->n();
// matrices for Runge-Kutta values:
mat k1_v(this->_rk4->dim(), n); // k1, velocity
mat k1_p(this->_rk4->dim(), n); // k1, position
mat k2_v(this->_rk4->dim(), n); // k2, velocity (etc.)
mat k2_p(this->_rk4->dim(), n);
mat k3_v(this->_rk4->dim(), n);
mat k3_p(this->_rk4->dim(), n);
mat k4_v(this->_rk4->dim(), n);
mat k4_p(this->_rk4->dim(), n);
// initial position and velocity for each celestial body
mat orig_v(this->_rk4->dim(), n);
mat orig_p(this->_rk4->dim(), n);
#pragma region k1
// calculate forces/accelerations based on current postions
this->_rk4->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_rk4->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// store initial position and velocity
orig_v.col(j) = *(cb->velocity);
orig_p.col(j) = *(cb->position);
// save values
k1_v.col(j) = step * cb->acc();
k1_p.col(j) = step * *(cb->velocity);
// advance to mid-point after k1
*(cb->velocity) = orig_v.col(j) + 0.5 * k1_v.col(j);
*(cb->position) = orig_p.col(j) + 0.5 * k1_p.col(j);
}
}
#pragma endregion
#pragma region k2
// calculate forces/accelerations based on current postions
this->_rk4->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_rk4->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// save values
k2_v.col(j) = step * cb->acc();
k2_p.col(j) = step * *(cb->velocity);
// switch to new mid-point using k2 instead
*(cb->velocity) = orig_v.col(j) + 0.5 * k2_v.col(j);
*(cb->position) = orig_p.col(j) + 0.5 * k2_p.col(j);
}
}
#pragma endregion
#pragma region k3
// calculate forces/accelerations based on current postions
this->_rk4->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_rk4->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// save values
k3_v.col(j) = step * cb->acc();
k3_p.col(j) = step * *(cb->velocity);
// switch to end-point
*(cb->velocity) = orig_v.col(j) + k3_v.col(j);
*(cb->position) = orig_p.col(j) + k3_p.col(j);
}
}
#pragma endregion
#pragma region k4
// calculate forces/accelerations based on current postions
this->_rk4->setForces();
for (int j = 0; j < n; j++) // for each celestial body
{
CelestialBody* cb = this->_rk4->body(j);
if (!cb->fixed) // a fixed celestial body will never move
{
// save values
k4_v.col(j) = step * cb->acc();
k4_p.col(j) = step * *(cb->velocity);
// finally, update position and velocity
*(cb->velocity) = orig_v.col(j) + (1.0 / 6.0)*(k1_v.col(j) + 2.0 * k2_v.col(j) + 2.0 * k3_v.col(j) + k4_v.col(j));
*(cb->position) = orig_p.col(j) + (1.0 / 6.0)*(k1_p.col(j) + 2.0 * k2_p.col(j) + 2.0 * k3_p.col(j) + k4_p.col(j));
}
}
#pragma endregion
}
