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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")

3
lib/objects.py
View File

@@ -34,6 +34,9 @@ class System:
def get_positions(self): #return the positions of the bodies
return np.array([body.q for body in self.bodylist])
def get_velocities(self): #return the positions of the bodies
return np.array([body.v for body in self.bodylist])
def get_momenta(self): #return the momenta of the bodies
return np.array([body.p for body in self.bodylist])

33
lib/plots.py
View File

@@ -14,6 +14,11 @@ class DynamicUpdate():
plt.ion()
def set_lims(self, factor=1.5):
self.ax.set_xlim(factor*self.min_x, factor*self.max_x)
self.ax.set_ylim(factor*self.min_x, factor*self.max_x)
self.ax.set_zlim(factor*self.min_x, factor*self.max_x)
def on_launch(self):
#Set up plot
self.fig = plt.figure()
@@ -21,27 +26,27 @@ class DynamicUpdate():
self.lines, = self.ax.plot([],[],[],'o')
#Autoscale on unknown axis and known lims on the other
self.ax.set_autoscaley_on(True)
self.ax.set_xlim(self.min_x, self.max_x)
self.ax.set_ylim(self.min_x, self.max_x)
self.ax.set_zlim(self.min_x, self.max_x)
self.set_lims()
#Other stuff
self.ax.grid()
#self.ax.set_aspect('equal')
def on_running(self, xdata, ydata, zdata, step=None, label=None):
values = np.sqrt(np.sum((np.array((xdata,ydata,zdata))**2).T,axis=1))
self.min_x, self.max_x = -np.abs(values).max(), np.abs(values).max()
self.set_lims()
#Update data (with the new _and_ the old points)
self.lines.set_data_3d(xdata, ydata, zdata)
if not label is None:
self.ax.set_title(label)
#Need both of these in order to rescale
self.ax.relim()
self.ax.autoscale_view()
#We need to draw *and* flush
self.fig.canvas.draw()
self.fig.canvas.flush_events()
if not step is None and step%100==0:
self.lines.set_data_3d(xdata, ydata, zdata)
if not label is None:
self.ax.set_title(label)
#Need both of these in order to rescale
self.ax.relim()
self.ax.autoscale_view()
#We need to draw *and* flush
self.fig.canvas.draw()
self.fig.canvas.flush_events()
if not step is None and step%100==0:
self.fig.savefig("tmp/{0:05d}.png".format(step),bbox_inches="tight")
self.fig.savefig("tmp/{0:05d}.png".format(step),bbox_inches="tight")
#Example
def __call__(self):