130 lines
4.3 KiB
Python
130 lines
4.3 KiB
Python
#!/usr/bin/python
|
|
# -*- coding:utf-8 -*-
|
|
"""
|
|
Hermite integrator
|
|
"""
|
|
|
|
|
|
from os import system
|
|
import numpy as np
|
|
from lib.plots import DynamicUpdate
|
|
from lib.units import *
|
|
|
|
|
|
def Update_a(dyn_syst): # update acceleration of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
body.a = np.zeros(3,dtype=np.longdouble)
|
|
for otherbody in dyn_syst.bodylist:
|
|
if body != otherbody:
|
|
rij = np.linalg.norm(body.q - otherbody.q)
|
|
body.a -= (body.q-otherbody.q)*G*otherbody.m/(rij**3)
|
|
|
|
|
|
def Update_j(dyn_syst): # update jerk of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
body.j = np.zeros(3,dtype=np.longdouble)
|
|
for otherbody in dyn_syst.bodylist:
|
|
if body != otherbody:
|
|
rij = np.linalg.norm(body.q - otherbody.q)
|
|
deltav = (body.v - otherbody.v)
|
|
deltar = (body.q - otherbody.q)
|
|
vr = deltav+3.*deltar*np.inner(deltav,deltar)/(rij**2)
|
|
body.j -= G*otherbody.m/(rij**3)*vr
|
|
|
|
|
|
def Predict(dyn_syst, dt): # update predicted q and v of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
body.qp = body.q+dt*body.v+((dt**2)*body.a/2.)+((dt**3)*body.j/ 6.)
|
|
body.vp = body.v+dt*body.a+((dt**2)*body.j/2.)
|
|
|
|
|
|
def Update_ap(dyn_syst): # update acceleration of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
body.ap = np.zeros(3,dtype=np.longdouble)
|
|
for otherbody in dyn_syst.bodylist:
|
|
if body != otherbody:
|
|
rij = np.linalg.norm(body.qp-otherbody.qp)
|
|
body.ap -= (body.qp-otherbody.qp)*G*otherbody.m/(rij**3)
|
|
|
|
|
|
def Update_jp(dyn_syst): # update jerk of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
body.jp = np.zeros(3,dtype=np.longdouble)
|
|
for otherbody in dyn_syst.bodylist:
|
|
if body != otherbody:
|
|
rij = np.linalg.norm(body.qp-otherbody.qp)
|
|
deltav = (body.vp-otherbody.vp)
|
|
deltar = (body.qp-otherbody.qp)
|
|
vr = deltav+3.*deltar*np.inner(deltav,deltar)/(rij**2)
|
|
body.jp -= G*otherbody.m/(rij**3)*vr
|
|
|
|
|
|
def Correct(dyn_syst, dt): # correct position and velocities of bodies in system
|
|
for body in dyn_syst.bodylist:
|
|
a2 = (6.*(body.a-body.ap)+dt*(4.*body.j+2.*body.jp))/(dt**2)
|
|
a3 = (12.*(body.a-body.ap)+dt*6.*(body.j+body.jp))/(dt**3)
|
|
|
|
body.q = body.qp+((dt**4)*a2/24.)+((dt**5)*a3/120.)
|
|
body.v = body.vp+((dt**3)*a2/6.)+((dt**4)*a3/24.)
|
|
|
|
|
|
def HPC(dyn_syst, dt): # update position and velocities of bodies in system with hermite predictor corrector
|
|
Update_a(dyn_syst)
|
|
Update_j(dyn_syst)
|
|
Predict(dyn_syst, dt)
|
|
Update_ap(dyn_syst)
|
|
Update_jp(dyn_syst)
|
|
Correct(dyn_syst, dt)
|
|
dyn_syst.time = dyn_syst.time + dt
|
|
|
|
|
|
def hermite(dyn_syst, bin_syst, duration, dt, recover_param=False,
|
|
display=False, savename=None, gif=False):
|
|
if display:
|
|
try:
|
|
system("mkdir tmp")
|
|
except IOError:
|
|
system("rm tmp/*")
|
|
d = DynamicUpdate(dyn_syst)
|
|
d.launch(dyn_syst.blackstyle)
|
|
|
|
N = np.ceil(duration/dt).astype(int)
|
|
E = np.zeros(N+1,dtype=np.longdouble)
|
|
L = np.zeros((N+1, 3),dtype=np.longdouble)
|
|
sma = np.zeros(N+1,dtype=np.longdouble)
|
|
ecc = np.zeros(N+1,dtype=np.longdouble)
|
|
phi = np.zeros(N+1,dtype=np.longdouble)
|
|
|
|
E[0] = dyn_syst.ECOM
|
|
L[0] = dyn_syst.LCOM
|
|
sma[0] = bin_syst.smaCOM
|
|
ecc[0] = bin_syst.eccCOM
|
|
phi[0] = dyn_syst.phi
|
|
|
|
for j in range(1,N+1):
|
|
HPC(dyn_syst, dt)
|
|
|
|
E[j] = dyn_syst.ECOM
|
|
L[j] = dyn_syst.LCOM
|
|
sma[j] = bin_syst.smaCOM
|
|
ecc[j] = bin_syst.eccCOM
|
|
phi[j] = dyn_syst.phi
|
|
|
|
if display and j % 10 == 0:
|
|
if gif:
|
|
step = j
|
|
else:
|
|
step = None
|
|
# display progression
|
|
if len(dyn_syst.bodylist) == 1:
|
|
d.on_running(step=step, label="{0:.2f} years".format(j*dt/yr))
|
|
else:
|
|
d.on_running(step=step, label="{0:.2f} years".format(j*dt/yr))
|
|
if display:
|
|
d.close()
|
|
if gif:
|
|
system("convert -delay 5 -loop 0 tmp/??????.png tmp/temp.gif && rm tmp/??????.png")
|
|
system("convert tmp/temp.gif -fuzz 10% -layers Optimize plots/{0:s}_dynsyst.gif".format(savename))
|
|
|
|
if recover_param:
|
|
return E, L, sma, ecc, phi |