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Added orbital element conversion code to swiftestio
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| ! Created by on 6/22/21. | ||
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| module orbel | ||
| private | ||
| public :: orbel_xv2el | ||
| use, intrinsic :: iso_fortran_env, only : I4B => int32, I8B => int64, SP => real32, DP => real64, QP => real128! Use the intrinsic kind definitions | ||
| implicit none | ||
| integer(I4B), parameter :: NDIM = 3 | ||
| integer(I4B), parameter :: ELLIPSE = -1 !! Symbolic names for orbit types - ellipse | ||
| integer(I4B), parameter :: PARABOLA = 0 !! Symbolic names for orbit types - parabola | ||
| integer(I4B), parameter :: HYPERBOLA = 1 !! Symbolic names for orbit types - hyperbola | ||
| contains | ||
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| pure subroutine orbel_xv2el(mu, x, v, a, e, inc, capom, omega, capm) | ||
| !! author: David A. Minton | ||
| !! | ||
| !! Compute osculating orbital elements from relative Cartesian position and velocity | ||
| !! All angular measures are returned in radians | ||
| !! If inclination < TINY, longitude of the ascending node is arbitrarily set to 0 | ||
| !! | ||
| !! If eccentricity < sqrt(TINY), argument of pericenter is arbitrarily set to 0 | ||
| !! | ||
| !! References: Danby, J. M. A. 1988. Fundamentals of Celestial Mechanics, (Willmann-Bell, Inc.), 201 - 206. | ||
| !! Fitzpatrick, P. M. 1970. Principles of Celestial Mechanics, (Academic Press), 69 - 73. | ||
| !! Roy, A. E. 1982. Orbital Motion, (Adam Hilger, Ltd.), 75 - 95 | ||
| !! | ||
| !! Adapted from David E. Kaufmann's Swifter routine: orbel_xv2el.f90 | ||
| !! Adapted from Martin Duncan's Swift routine orbel_xv2el.f | ||
| implicit none | ||
| ! Arguments | ||
| real(DP), intent(in) :: mu | ||
| real(DP), dimension(:), intent(in) :: x, v | ||
| real(DP), intent(out) :: a, e, inc, capom, omega, capm | ||
| !f2py intent(in) mu | ||
| !f2py intent(in) x | ||
| !f2py intent(in) v | ||
| !f2py intent(out) a | ||
| !f2py intent(out) e | ||
| !f2py intent(out) inc | ||
| !f2py intent(out) capom | ||
| !f2py intent(out) omega | ||
| !f2py intent(out) capm | ||
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| ! Internals | ||
| integer(I4B) :: iorbit_type | ||
| real(DP) :: r, v2, h2, h, rdotv, energy, fac, u, w, cw, sw, face, cape, tmpf, capf | ||
| real(DP), dimension(NDIM) :: hvec | ||
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| a = 0.0_DP | ||
| e = 0.0_DP | ||
| inc = 0.0_DP | ||
| capom = 0.0_DP | ||
| omega = 0.0_DP | ||
| capm = 0.0_DP | ||
| r = sqrt(dot_product(x(:), x(:))) | ||
| v2 = dot_product(v(:), v(:)) | ||
| hvec = x(:) .cross. v(:) | ||
| h2 = dot_product(hvec(:), hvec(:)) | ||
| h = sqrt(h2) | ||
| if (h2 == 0.0_DP) return | ||
| rdotv = dot_product(x(:), v(:)) | ||
| energy = 0.5_DP * v2 - mu / r | ||
| fac = hvec(3) / h | ||
| if (fac < -1.0_DP) then | ||
| inc = PI | ||
| else if (fac < 1.0_DP) then | ||
| inc = acos(fac) | ||
| end if | ||
| fac = sqrt(hvec(1)**2 + hvec(2)**2) / h | ||
| if (fac**2 < VSMALL) then | ||
| u = atan2(x(2), x(1)) | ||
| if (hvec(3) < 0.0_DP) u = -u | ||
| else | ||
| capom = atan2(hvec(1), -hvec(2)) | ||
| u = atan2(x(3) / sin(inc), x(1) * cos(capom) + x(2) * sin(capom)) | ||
| end if | ||
| if (capom < 0.0_DP) capom = capom + TWOPI | ||
| if (u < 0.0_DP) u = u + TWOPI | ||
| if (abs(energy * r / mu) < sqrt(VSMALL)) then | ||
| iorbit_type = PARABOLA | ||
| else | ||
| a = -0.5_DP * mu / energy | ||
| if (a < 0.0_DP) then | ||
| fac = -h2 / (mu * a) | ||
| if (fac > VSMALL) then | ||
| iorbit_type = HYPERBOLA | ||
| else | ||
| iorbit_type = PARABOLA | ||
| end if | ||
| else | ||
| iorbit_type = ELLIPSE | ||
| end if | ||
| end if | ||
| select case (iorbit_type) | ||
| case (ELLIPSE) | ||
| fac = 1.0_DP - h2 / (mu * a) | ||
| if (fac > VSMALL) then | ||
| e = sqrt(fac) | ||
| cape = 0.0_DP | ||
| face = (a - r) / (a * e) | ||
| if (face < -1.0_DP) then | ||
| cape = PI | ||
| else if (face < 1.0_DP) then | ||
| cape = acos(face) | ||
| end if | ||
| if (rdotv < 0.0_DP) cape = TWOPI - cape | ||
| fac = 1.0_DP - e * cos(cape) | ||
| cw = (cos(cape) - e) / fac | ||
| sw = sqrt(1.0_DP - e**2) * sin(cape) / fac | ||
| w = atan2(sw, cw) | ||
| if (w < 0.0_DP) w = w + TWOPI | ||
| else | ||
| cape = u | ||
| w = u | ||
| end if | ||
| capm = cape - e * sin(cape) | ||
| case (PARABOLA) | ||
| a = 0.5_DP * h2 / mu | ||
| e = 1.0_DP | ||
| w = 0.0_DP | ||
| fac = 2 * a / r - 1.0_DP | ||
| if (fac < -1.0_DP) then | ||
| w = PI | ||
| else if (fac < 1.0_DP) then | ||
| w = acos(fac) | ||
| end if | ||
| if (rdotv < 0.0_DP) w = TWOPI - w | ||
| tmpf = tan(0.5_DP * w) | ||
| capm = tmpf * (1.0_DP + tmpf * tmpf / 3.0_DP) | ||
| case (HYPERBOLA) | ||
| e = sqrt(1.0_DP + fac) | ||
| tmpf = max((a - r) / (a * e), 1.0_DP) | ||
| capf = log(tmpf + sqrt(tmpf**2 - 1.0_DP)) | ||
| if (rdotv < 0.0_DP) capf = -capf | ||
| fac = e * cosh(capf) - 1.0_DP | ||
| cw = (e - cosh(capf)) / fac | ||
| sw = sqrt(e * e - 1.0_DP) * sinh(capf) / fac | ||
| w = atan2(sw, cw) | ||
| if (w < 0.0_DP) w = w + TWOPI | ||
| capm = e * sinh(capf) - capf | ||
| end select | ||
| omega = u - w | ||
| if (omega < 0.0_DP) omega = omega + TWOPI | ||
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| return | ||
| end subroutine orbel_xv2el | ||
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| end module orbel |