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import pandas as pd
import numpy as np
class LowLevel():
def __init__(self, j):
self.j = j
def initial(self):
j = self.j
#init parameters
h, b, n, u = 0.1, None, None, None
x, y, z, px, py, pz = None, 0.1, 0.001, 0.01, None, 0.0001
xa, ya, za, pxa, pya, pza = None, None, None, None, None, None
if j == 1:
b = 5.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 10.0
py = 0.5
elif j == 2:
b = 3.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 8.3
py = 0.6
elif j == 3:
b = 3.0 / 2
x = 12.0
py = 0.4
elif j == 4:
b = 7.0 / 4
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 15.0
py = 0.35
elif j == 5:
b = 1.0
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 18.0
py = 0.3
elif j == 6:
b = 3.0 / 5
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 20.0
py = 0.25
elif j == 7:
b = 5.0 / 7
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 22.0
py = 0.22
elif j == 8:
b = 2.0
x = 26.0
py = 0.2
elif j == 9:
b = 0.5
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 30.0
y = 0.5
z = 0.1
pz = 0.01
elif j == 10:
b = 5.0
n = b / (1 + b) ** 2
u = 1.0 / (1.0 / b + b + 2.0)
x = 35.0
y = 2.0
z = 0.1
pz = 0.03
py = 0.15
xa, ya, za, pxa, pya, pza = x, y, z, px, py, pz
return j, h, b, n, x, y, z, xa, ya, za, px, py, pz, pxa, pya, pza
def f(self, x, y, z, px, py, pz, b):
n = b / (1 + b)**2
u = 1 / (1 / b + b + 2)
ht = px**2 / 2 + py**2 / 2 + pz**2 / 2
hv = -1 / (x**2 + y**2 + z**2)**(1/2)
h1pn = 1/(2*x**2 + 2*y**2 + 2*z**2) - (((u + 3)*(px**2 + py**2 +pz**2))/2 + (u*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/ (x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2))**2)/2)/(x**2 + y**2 + z**2)**(1/2) + ((3*u)/8 -1/8)*(px**2 + py**2 + pz**2)**2
e = ht + hv + h1pn
vnpx=px
v1pnpx=4*px*((3*n)/8 - 1/8)*(px**2 + py**2 + pz**2) - (px*(n + 3) + (n*x*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2)))/(x**2 + y**2 + z**2)**(1/2))/(x**2 + y**2 + z**2)**(1/2)
vpx=vnpx+v1pnpx
vnpy=py
v1pnpy=4*py*((3*n)/8 - 1/8)*(px**2 + py**2 + pz**2) - (py*(n + 3) + (n*y*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2)))/(x**2 + y**2 + z**2)**(1/2))/(x**2 + y**2 + z**2)**(1/2)
vpy=vnpy+v1pnpy
vnpz=pz
v1pnpz=4*pz*((3*n)/8 - 1/8)*(px**2 + py**2 + pz**2) - (pz*(n + 3) + (n*z*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2)))/(x**2 + y**2 + z**2)**(1/2))/(x**2 + y**2 + z**2)**(1/2)
vpz=vnpz+v1pnpz
vnx=x/(x**2 + y**2 + z**2)**(3/2)
v1pnx=(x*((n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 +y**2 + z**2)**(1/2))**2)/2 + ((n + 3)*(px**2 + py**2 + pz**2))/2))/(x**2 + y**2 + z**2)**(3/2) -(4*x)/(2*x**2 + 2*y**2 + 2*z**2)**2 + (n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2))*((px*x**2)/(x**2 + y**2 + z**2)**(3/2) -px/(x**2 + y**2 + z**2)**(1/2) + (py*x*y)/(x**2 + y**2 + z**2)**(3/2) + (pz*x*z)/(x**2 + y**2 +z**2)**(3/2)))/(x**2 + y**2 + z**2)**(1/2)
vx=vnx+v1pnx
vny=y/(x**2 + y**2 + z**2)**(3/2)
v1pny=(y*((n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 +y**2 + z**2)**(1/2))**2)/2 + ((n + 3)*(px**2 + py**2 + pz**2))/2))/(x**2 + y**2 + z**2)**(3/2) -(4*y)/(2*x**2 + 2*y**2 + 2*z**2)**2 + (n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2))*((py*y**2)/(x**2 + y**2 + z**2)**(3/2) -py/(x**2 + y**2 + z**2)**(1/2) + (px*x*y)/(x**2 + y**2 + z**2)**(3/2) + (pz*y*z)/(x**2 + y**2 +z**2)**(3/2)))/(x**2 + y**2 + z**2)**(1/2)
vy=vny+v1pny
vnz=z/(x**2 + y**2 + z**2)**(3/2)
v1pnz=(z*((n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 +y**2 + z**2)**(1/2))**2)/2 + ((n + 3)*(px**2 + py**2 + pz**2))/2))/(x**2 + y**2 + z**2)**(3/2) -(4*z)/(2*x**2 + 2*y**2 + 2*z**2)**2 + (n*((px*x)/(x**2 + y**2 + z**2)**(1/2) + (py*y)/(x**2 + y**2 + z**2)**(1/2) + (pz*z)/(x**2 + y**2 + z**2)**(1/2))*((pz*z**2)/(x**2 + y**2 + z**2)**(3/2) -pz/(x**2 + y**2 + z**2)**(1/2) + (px*x*z)/(x**2 + y**2 + z**2)**(3/2) + (py*y*z)/(x**2 + y**2 +z**2)**(3/2)))/(x**2 + y**2 + z**2)**(1/2)
vz=vnz+v1pnz
return vx,vy,vz,vpx,vpy,vpz,e
def rejust(self, x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza):
x = (x + xa) / 2
y = (y + ya) / 2
z = (z + za) / 2
px = (px + pxa) / 2
py = (py + pya) / 2
pz = (pz + pza) / 2
xa = x
ya = y
za = z
pxa = px
pya = py
pza = pz
return x,y,z,px,py,pz,xa,ya,za,pxa,pya,pza
def symplectic(self, h, x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza, b):
vxa, vya, vza, vpx, vpy, vpz, e = self.f(xa, ya, za, px, py, pz, b)
x = x + h / 2 * vpx
y = y + h / 2 * vpy
z = z + h / 2 * vpz
pxa = pxa - h / 2 * vxa
pya = pya - h / 2 * vya
pza = pza - h / 2 * vza
vx, vy, vz, vpxa, vpya, vpza, e = self.f(x, y, z, pxa, pya, pza, b)
xa = xa + h * vpxa
ya = ya + h * vpya
za = za + h * vpza
px = px - h * vx
py = py - h * vy
pz = pz - h * vz
vxa, vya, vza, vpx, vpy, vpz, e = self.f(xa, ya, za, px, py, pz, b)
x = x + h / 2 * vpx
y = y + h / 2 * vpy
z = z + h / 2 * vpz
pxa = pxa - h / 2 * vxa
pya = pya - h / 2 * vya
pza = pza - h / 2 * vza
return x, y, z, px, py, pz, xa, ya, za, pxa, pya, pza |