def __r_mtx_p(self):
""" precession（歳差）変換行列（J2000.0 用）
* 歳差の変換行列
P(ε, ψ, φ, γ) = R1(-ε) * R3(-ψ) * R1(φ) * R3(γ)
但し、R1, R2, R3 は x, y, z 軸の回転。
| 1 0 0 | | cosθ sinθ 0 |
R1(θ) = | 0 cosθ sinθ |, R3(θ) = | -sinθ cosθ 0 |
| 0 -sinθ cosθ | | 0 0 1 |
| P_11 P_12 P_13 |
P(ε, ψ, φ, γ) = | P_21 P_22 P_23 | とすると、
| P_31 P_32 P_33 |
P_11 = cosψcosγ + sinψcosφsinγ
P_12 = cosψsinγ - sinψcosφcosγ
P_13 = -sinψsinφ
P_21 = cosεsinψcosγ - (cosεcosψcosφ + sinεsinφ)sinγ
P_22 = cosεsinψcosγ + (cosεcosψcosφ + sinεsinφ)cosγ
P_23 = cosεcosψsinφ - sinεcosφ
P_31 = sinεsinψcosγ - (sinεcosψcosφ - cosεsinφ)sinγ
P_32 = sinεsinψcosγ + (sinεcosψcosφ - cosεsinφ)cosγ
P_33 = sinεcosψsinφ + cosεcosφ
:return np.matrix r: 変換行列
"""
try:
gam = self.__gamma_p()
phi = self.__phi_p()
psi = self.__psi_p()
r = lmtx.r_z(gam)
r = lmtx.r_x(phi, r)
r = lmtx.r_z(-psi, r)
r = lmtx.r_x(-self.eps, r)
return r
except Exception as e:
raise
def __r_mtx_n(self):
""" nutation（章動）変換行列
* IAU 2000A nutation with adjustments to match the IAU 2006 precession.
:return np.matrix r: 変換行列
"""
try:
r = lmtx.r_x(self.eps)
r = lmtx.r_z(-self.dpsi, r)
r = lmtx.r_x(-self.eps - self.deps, r)
return r
except Exception as e:
raise
def __r_mtx_b(self):
""" Bias 変換行列（一般的な理論）
* 赤道座標(J2000.0)の極は ICRS の極に対して12時（x軸のマイナス側）の
方向へ 17.3±0.2 mas、18時（y軸のマイナス側）の方向へ 5.1±0.2 mas
ズレているので、変換する。
さらに、平均分点への変換はICRSでの赤経を78±10 mas、天の極を中心に
回転させる。
18時の方向の変換はx軸を-5.1mas回転
| 1 0 0 |
R1(θ ) = | 0 cosθ sinθ |
| 0 -sinθ cosθ |
12時の方向の変換はy軸を-17.3mas回転
| cosθ 0 -sinθ |
R2(θ ) = | 0 1 0 |
| sinθ 0 cosθ |
天の極を中心に78.0mas回転
| cosθ sinθ 0 |
R3(θ ) = | -sinθ cosθ 0 |
| 0 0 1 |
:return np.matrix r: 回転行列
"""
try:
r = lmtx.r_x( -5.1 * lcst.MAS2R)
r = lmtx.r_y(-17.3 * lcst.MAS2R, r)
r = lmtx.r_z( 78.0 * lcst.MAS2R, r)
return r
except Exception as e:
raise
def __r_mtx_pn(self):
""" Precession + Nutation 変換行列
* IAU 2000A nutation with adjustments to match the IAU 2006 precession.
:return np.matrix r: 変換行列
"""
try:
gam = self.__gamma_p()
phi = self.__phi_p()
psi = self.__psi_p()
r = lmtx.r_z(gam)
r = lmtx.r_x(phi, r)
r = lmtx.r_z(-psi - self.dpsi, r)
r = lmtx.r_x(-self.eps - self.deps, r)
return r
except Exception as e:
raise
def __r_mtx_bpn(self):
""" Bias + Precession + Nutation 変換行列
* IAU 2006 (Fukushima-Williams 4-angle formulation) 理論
:return np.matrix r: 変換行列
"""
try:
gam = self.__gamma_bp()
phi = self.__phi_bp()
psi = self.__psi_bp()
r = lmtx.r_z(gam)
r = lmtx.r_x(phi, r)
r = lmtx.r_z(-psi - self.dpsi, r)
r = lmtx.r_x(-self.eps - self.deps, r)
return r
except Exception as e:
raise
def rect_ec2eq(rect, eps):
""" 直交座標：黄道座標 -> 赤道座標.
:param list rect: 黄道直交座標
:param float eps: 黄道傾斜角 (Unit: rad)
:return list : 赤道直交座標
"""
try:
mtx_rect = np.matrix([rect]).transpose()
r_mtx = lmtx.r_x(-eps)
return lmtx.rotate(r_mtx, mtx_rect).A1.tolist()
except Exception as e:
raise