From fff1832e611dae8aa835344f8e24d3b8ee89dcc9 Mon Sep 17 00:00:00 2001 From: Thibault Barnouin Date: Fri, 5 Nov 2021 17:12:16 +0100 Subject: [PATCH] modify leapfrog to take velocities instead of momenta, add new initial conditions --- lib/integrator.py | 41 ++++++++++++++++++++--------------------- lib/objects.py | 3 +++ lib/plots.py | 33 +++++++++++++++++++-------------- main.py | 15 +++++++++------ plots/dynsyst.gif | Bin 78252 -> 358145 bytes 5 files changed, 51 insertions(+), 41 deletions(-) diff --git a/lib/integrator.py b/lib/integrator.py index 7a9c971..65415a9 100755 --- a/lib/integrator.py +++ b/lib/integrator.py @@ -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") diff --git a/lib/objects.py b/lib/objects.py index a919b5a..6f065d2 100755 --- a/lib/objects.py +++ b/lib/objects.py @@ -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]) diff --git a/lib/plots.py b/lib/plots.py index 9a61177..9607a54 100755 --- a/lib/plots.py +++ b/lib/plots.py @@ -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): diff --git a/main.py b/main.py index 8236eab..3e6eadb 100755 --- a/main.py +++ b/main.py @@ -12,7 +12,8 @@ globals()['au'] = 1.5e11 #Astronomical unit in m def main(): #initialisation - m = np.array([1., 1., 0.1])*Ms # Masses in Solar mass + m = np.array([1, 1, 0.1])*Ms # Masses in Solar mass + mu = m[0]*m[1]/(m[0]+m[1]) a = np.array([1., 1., 5.])*au # Semi-major axis in astronomical units psi = np.array([0., 0., 80.])*np.pi/180. # Inclination of the orbital plane in degrees @@ -21,9 +22,9 @@ def main(): x3 = np.array([np.cos(psi[2]), 0., np.sin(psi[2])])*a[2] q = np.array([x1, x2, x3]) - v1 = np.array([0, -np.sqrt(G*Ms/np.sqrt(np.sum(x1**2))), 0]) - v2 = np.array([0, np.sqrt(G*Ms/np.sqrt(np.sum(x2**2))), 0]) - v3 = np.array([0, np.sqrt(G*Ms*(2./np.sqrt(np.sum(x3**2))-1./a[2])), 0]) + v1 = np.array([0., -np.sqrt(G*mu/np.sqrt(np.sum(x1**2))), 0]) + v2 = np.array([0., np.sqrt(G*mu/np.sqrt(np.sum(x2**2))), 0.]) + v3 = np.array([0., np.sqrt(G*(m[0]+m[1])*(2./np.sqrt(np.sum(x3**2))-1./a[2])), 0.]) v = np.array([v1, v2, v3]) bodylist = [] @@ -32,8 +33,9 @@ def main(): dyn_syst = System(bodylist) dyn_syst.COMShift() - duration, step = 100, 0.01 - E, L = frogleap(duration, step, dyn_syst, recover_param=True, display=True) + duration, step = 0.5*3e7, 1e1 + E, L = frogleap(duration, step, dyn_syst, recover_param=True)#, display=True) + fig1 = plt.figure(figsize=(30,15)) ax1 = fig1.add_subplot(111) ax1.plot(np.arange(E.shape[0])/duration, E, label=r"$E_m$") @@ -45,6 +47,7 @@ def main(): ax2.legend() fig2.savefig("plots/L2.png",bbox_inches="tight") plt.show(block=True) + return 0 if __name__ == '__main__': diff --git a/plots/dynsyst.gif b/plots/dynsyst.gif index cd48ea4dfe321474ccf7286c2d55f7672d5dbd1f..882e0ebfe9d71828cdc267548e0197f9d2ee1619 100644 GIT binary patch literal 358145 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