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modify leapfrog to take velocities instead of momenta, add new initial conditions

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Thibault Barnouin
2021-11-05 17:12:16 +01:00
parent d5f948f4a1
commit fff1832e61
5 changed files with 51 additions and 41 deletions
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41
lib/integrator.py
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@@ -14,18 +14,18 @@ globals()['G'] = 6.67e-11 #Gravitational constant in SI units
globals()['Ms'] = 2e30 #Solar mass in kg
globals()['au'] = 1.5e11 #Astronomical unit in m
def dp_dt(m_array, q_array):
def dv_dt(m_array, q_array):
"""
Time derivative of the momentum, given by the position derivative of the Hamiltonian.
dp/dt = -dH/dq
Time derivative of the velocity, given by the position derivative of the Hamiltonian.
dv/dt = -1/m*dH/dq
"""
dp_array = np.zeros(q_array.shape)
dv_array = np.zeros(q_array.shape)
for i in range(q_array.shape[0]):
q_j = np.delete(q_array, i, 0)
m_j = np.delete(m_array, i, 0)
dp_array[i] = -G*m_array[i]*np.sum(m_j/np.sum(np.sqrt(np.sum((q_j-q_array[i])**2, axis=0)))**3*(q_j-q_array[i]), axis=0)
dp_array[np.isnan(dp_array)] = 0.
return dp_array
dv_array[i] = -G*np.sum((m_j*(q_j-q_array[i])).T/np.sqrt(np.sum((q_j-q_array[i])**2, axis=1))**3, axis=1).T
dv_array[np.isnan(dv_array)] = 0.
return dv_array
def frogleap(duration, step, dyn_syst, recover_param=False, display=False):
"""
@@ -34,10 +34,10 @@ def frogleap(duration, step, dyn_syst, recover_param=False, display=False):
"""
N = np.ceil(duration/step).astype(int)
q_array = dyn_syst.get_positions()
p_array = dyn_syst.get_momenta()
v_array = dyn_syst.get_velocities()
masses = dyn_syst.get_masses()
m_array = np.ones(p_array.shape)
for i in range(p_array.shape[0]):
m_array = np.ones(q_array.shape)
for i in range(q_array.shape[0]):
m_array[i,:] = masses[i]
E = np.zeros(N)
@@ -49,32 +49,31 @@ def frogleap(duration, step, dyn_syst, recover_param=False, display=False):
except IOError:
system("rm tmp/*")
d = DynamicUpdate()
d.min_x, d.max_x = -1.5*np.abs(q_array).max(), +1.5*np.abs(q_array).max()
d.on_launch()
for j in range(N):
# half-step drift
q_array, p_array = q_array + step/2*p_array/m_array , p_array
q_array, v_array = q_array + step/2*v_array , v_array
# full-step kick
q_array, p_array = q_array , p_array - step*dp_dt(m_array, q_array)
q_array, v_array = q_array , v_array - step*dv_dt(m_array, q_array)
# half-step drift
q_array, p_array = q_array + step/2*p_array/m_array , p_array
q_array, v_array = q_array + step/2*v_array , v_array
for i, body in enumerate(dyn_syst.bodylist):
body.q = q_array[i]
body.p = p_array[i]
if body.m != 0.:
body.v = body.p/body.m
body.v = v_array[i]
body.p = body.v*body.m
dyn_syst.COMShift()
E[j] = dyn_syst.Eval()
L[j] = dyn_syst.Lval()
if display:
# In center of mass frame
q_cm = np.array([0,0,0])#np.sum(m_array*q_array, axis=0)/masses.sum()
# display progression
d.on_running(q_array[:,0]-q_cm[0], q_array[:,1]-q_cm[1], q_array[:,2]-q_cm[2], step=j, label="step {0:d}/{1:d}".format(j,N))
time.sleep(1e-4)
if len(dyn_syst.bodylist) == 1:
d.on_running(q_array[0], q_array[1], q_array[2], step=j, label="step {0:d}/{1:d}".format(j,N))
else:
d.on_running(q_array[:,0], q_array[:,1], q_array[:,2], step=j, label="step {0:d}/{1:d}".format(j,N))
time.sleep(1e-5)
if display:
system("convert -delay 5 -loop 0 tmp/?????.png tmp/temp.gif && rm tmp/?????.png")
system("convert tmp/temp.gif -fuzz 30% -layers Optimize plots/dynsyst.gif && rm tmp/temp.gif")