def HS2011_Omega_SO_3p5PN_pt7(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(181 * m1 * m2 / 16 + 95 * m2**2 / 4 + 75 * m2**3 /
(8 * m1)) * cross(n12U, p1U)[i] -
(21 * m1**2 / 2 + 473 * m1 * m2 / 16 + 63 * m2**2 / 4) *
cross(n12U, p2U)[i]) / r12**4
return Omega1
def f_H_SS_S1S2_3PN(m1, m2, n12U, S1U, S2U, p1U, p2U, r12):
global H_SS_S1S2_3PN
H_SS_S1S2_3PN = (
+div(3, 2) *
(dot(cross(p1U, S1U), n12U) * dot(cross(p2U, S2U), n12U)) + 6 *
(dot(cross(p2U, S1U), n12U) * dot(cross(p1U, S2U), n12U)) -
15 * dot(S1U, n12U) * dot(S2U, n12U) * dot(p1U, n12U) * dot(p2U, n12U)
- 3 * dot(S1U, n12U) * dot(S2U, n12U) * dot(p1U, p2U) +
3 * dot(S1U, p2U) * dot(S2U, n12U) * dot(p1U, n12U) +
3 * dot(S2U, p1U) * dot(S1U, n12U) * dot(p2U, n12U) +
3 * dot(S1U, p1U) * dot(S2U, n12U) * dot(p2U, n12U) +
3 * dot(S2U, p2U) * dot(S1U, n12U) * dot(p1U, n12U) - div(1, 2) *
dot(S1U, p2U) * dot(S2U, p1U) + dot(S1U, p1U) * dot(S2U, p2U) -
3 * dot(S1U, S2U) * dot(p1U, n12U) * dot(p2U, n12U) +
div(1, 2) * dot(S1U, S2U) * dot(p1U, p2U)) / (2 * m1 * m2 * r12**3)
H_SS_S1S2_3PN += (-dot(cross(p1U, S1U), n12U) * dot(cross(p1U, S2U), n12U)
+ dot(S1U, S2U) * dot(p1U, n12U)**2 -
dot(S1U, n12U) * dot(S2U, p1U) * dot(p1U, n12U)) * 3 / (
2 * m1**2 * r12**3)
H_SS_S1S2_3PN += (-dot(cross(p2U, S2U), n12U) * dot(cross(p2U, S1U), n12U)
+ dot(S1U, S2U) * dot(p2U, n12U)**2 -
dot(S2U, n12U) * dot(S1U, p1U) * dot(p2U, n12U)) * 3 / (
2 * m2**2 * r12**3)
H_SS_S1S2_3PN += (+dot(S1U, S2U) - 2 * dot(S1U, n12U) *
dot(S2U, n12U)) * 6 * (m1 + m2) / r12**4
def f_Omega_SO_2p5PN(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(+(-div(11, 2) * m2 - 5 * m2 ** 2 / m1) * cross(n12U, p1U)[i]
+ (6 * m1 + div(15, 2) * m2) * cross(n12U, p2U)[i]) / r12 ** 3
+ (+(-div(5, 8) * m2 * dot(p1U, p1U) / m1 ** 3
- div(3, 4) * dot(p1U, p2U) / m1 ** 2
+ div(3, 4) * dot(p2U, p2U) / (m1 * m2)
- div(3, 4) * dot(n12U, p1U) * dot(n12U, p2U) / m1 ** 2
- div(3, 2) * dot(n12U, p2U) ** 2 / (m1 * m2)) * cross(n12U, p1U)[i]
+ (dot(p1U, p2U) / (m1 * m2) + 3 * dot(n12U, p1U) * dot(n12U, p2U) / (m1 * m2)) *
cross(n12U, p2U)[i]
+ (div(3, 4) * dot(n12U, p1U) / m1 ** 2 - 2 * dot(n12U, p2U) / (m1 * m2)) * cross(p1U, p2U)[
i]) / r12 ** 2)
return Omega1
def HS2011_Omega_SO_3p5PN_pt6(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-(8 / m1 + 9 * m2 / (2 * m1**2)) * dot(n12U, p1U) +
(59 / (4 * m1) + 27 / (2 * m2)) * dot(n12U, p2U)) *
cross(p1U, p2U)[i]) / r12**3
return Omega1
def HS2011_Omega_SO_3p5PN_pt3(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-9*dot(n12U,p1U)*dot(p1U,p1U)/(16*m1**4)
+dot(p1U,p1U)*dot(n12U,p2U)/(m1**3*m2)
+27*dot(n12U,p1U)*dot(n12U,p2U)**2/(16*m1**2*m2**2)
-dot(n12U,p2U)*dot(p1U,p2U)/(8*m1**2*m2**2)
-5*dot(n12U,p1U)*dot(p2U,p2U)/(16*m1**2*m2**2))*cross(p1U,p2U)[i])/r12**2
return Omega1
def HS2011_Omega_SO_3p5PN_pt5(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(+4*dot(n12U,p1U)**2/m1
+13*dot(p1U,p1U)/(2*m1)
+5*dot(n12U,p2U)**2/m2
+53*dot(p2U,p2U)/(8*m2)
-(211/(8*m1) + 22/m2)*dot(n12U,p1U)*dot(n12U,p2U)
-(47/(8*m1) + 5/m2)*dot(p1U,p2U))*cross(n12U,p2U)[i])/r12**3
return Omega1
def HS2011_Omega_SO_3p5PN_pt4(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-3*m2*dot(n12U,p1U)**2/(2*m1**2)
+((-3*m2)/(2*m1**2) + 27*m2**2/(8*m1**3))*dot(p1U,p1U)
+(177/(16*m1) + 11/m2)*dot(n12U,p2U)**2
+(11/(2*m1) + 9*m2/(2*m1**2))*dot(n12U,p1U)*dot(n12U,p2U)
+(23/(4*m1) + 9*m2/(2*m1**2))*dot(p1U,p2U)
-(159/(16*m1) + 37/(8*m2))*dot(p2U,p2U))*cross(n12U,p1U)[i])/r12**3
return Omega1
def f_H_SSS_3PN_pt(m1,m2, nU, S1U,S2U, p1U,p2U, r):
p2_minus_m2_over_4m1_p1 = ixp.zerorank1()
for i in range(3):
p2_minus_m2_over_4m1_p1[i] = p2U[i] - m2/(4*m1)*p1U[i]
H_SSS_3PN_pt = (+div(3,2)*(+dot(S1U,S1U)*dot(S2U,cross(nU,p1U))
+dot(S1U,nU)*dot(S2U,cross(S1U,p1U))
-5*dot(S1U,nU)**2*dot(S2U,cross(nU,p1U))
+dot(nU,cross(S1U,S2U))*(+dot(S1U,p1U)
-5*dot(S1U,nU)*dot(p1U,nU)))
-3*m1/(2*m2)*( +dot(S1U,S1U) *dot(S2U,cross(nU,p2U))
+2*dot(S1U,nU) *dot(S2U,cross(S1U,p2U))
-5*dot(S1U,nU)**2*dot(S2U,cross(nU,p2U)))
-dot(cross(S1U,nU),p2_minus_m2_over_4m1_p1)*(dot(S1U,S1U) - 5*dot(S1U,nU)**2))/(m1**2*r**4)
return H_SSS_3PN_pt
def HS2011_Omega_SO_3p5PN_pt2(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (+(-3*dot(n12U,p1U)*dot(n12U,p2U)*dot(p1U,p1U)/(2*m1**3*m2)
-15*dot(n12U,p1U)**2*dot(n12U,p2U)**2/(4*m1**2*m2**2)
+3*dot(p1U,p1U)*dot(n12U,p2U)**2/(4*m1**2*m2**2)
-dot(p1U,p1U)*dot(p1U,p2U)/(2*m1**3*m2)
+dot(p1U,p2U)**2/(2*m1**2*m2**2)
+3*dot(n12U,p1U)**2*dot(p2U,p2U)/(4*m1**2*m2**2)
-dot(p1U,p1U)*dot(p2U,p2U)/(4*m1**2*m2**2)
-3*dot(n12U,p1U)*dot(n12U,p2U)*dot(p2U,p2U)/(2*m1*m2**3)
-dot(p1U,p2U)*dot(p2U,p2U)/(2*m1*m2**3))*cross(n12U,p2U)[i])/r12**2
return Omega1
def HS2011_Omega_SO_3p5PN_pt1(m1,m2, n12U, p1U,p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = ((+7*m2*dot(p1U,p1U)**2/(16*m1**5)
+9*dot(n12U,p1U)*dot(n12U,p2U)*dot(p1U,p1U)/(16*m1**4)
+3*dot(p1U,p1U)*dot(n12U,p2U)**2/(4*m1**3*m2)
+45*dot(n12U,p1U)*dot(n12U,p2U)**3/(16*m1**2*m2**2)
+9*dot(p1U,p1U)*dot(p1U,p2U)/(16*m1**4)
-3*dot(n12U,p2U)**2*dot(p1U,p2U)/(16*m1**2*m2**2)
-3*dot(p1U,p1U)*dot(p2U,p2U)/(16*m1**3*m2)
-15*dot(n12U,p1U)*dot(n12U,p2U)*dot(p2U,p2U)/(16*m1**2*m2**2)
+3*dot(n12U,p2U)**2*dot(p2U,p2U)/(4*m1*m2**3)
-3*dot(p1U,p2U)*dot(p2U,p2U)/(16*m1**2*m2**2)
-3*dot(p2U,p2U)**2/(16*m1*m2**3))*cross(n12U,p1U)[i])/r12**2
return Omega1
def f_Omega1(m1, m2, n12U, p1U, p2U, r12):
Omega1 = ixp.zerorank1()
for i in range(3):
Omega1[i] = (div(3, 2) * m2 / m1 * cross(n12U, p1U)[i] -
2 * cross(n12U, p2U)[i]) / r12**2
return Omega1
