compute_libration_points_v2 Subroutine

public subroutine compute_libration_points_v2(mu, r1, r2, r3, r4, r5)

Uses

  • proc~~compute_libration_points_v2~~UsesGraph proc~compute_libration_points_v2 crtbp_module::compute_libration_points_v2 module~math_module math_module proc~compute_libration_points_v2->module~math_module module~kind_module kind_module module~math_module->module~kind_module module~numbers_module numbers_module module~math_module->module~numbers_module iso_fortran_env iso_fortran_env module~kind_module->iso_fortran_env module~numbers_module->module~kind_module

Compute the coordinates of the libration points (L1,L2,L3,L4,L5).

This is just an alternate version of compute_libration_points.

Reference

  • J.S. Parker, R.L. Anderson, "Low-Energy Lunar Trajectory Design", 2014. (Appendix A.5)

Note

The coordinate are w.r.t. the barycenter of the system.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: mu

CRTBP parameter
real(kind=wp), intent(out), optional :: r1

L1 x coordinate
real(kind=wp), intent(out), optional :: r2

L2 x coordinate
real(kind=wp), intent(out), optional :: r3

L3 x coordinate
real(kind=wp), intent(out), optional, dimension(2) :: r4

L4 [x,y] coordinates
real(kind=wp), intent(out), optional, dimension(2) :: r5

L5 [x,y] coordinates

Calls

proc~~compute_libration_points_v2~~CallsGraph proc~compute_libration_points_v2 crtbp_module::compute_libration_points_v2 proc~compute_libration_points crtbp_module::compute_libration_points proc~compute_libration_points_v2->proc~compute_libration_points proc~cube_root math_module::cube_root proc~compute_libration_points_v2->proc~cube_root proc~compute_libration_points->proc~cube_root

Called by

proc~~compute_libration_points_v2~~CalledByGraph proc~compute_libration_points_v2 crtbp_module::compute_libration_points_v2 proc~crtbp_test crtbp_module::crtbp_test proc~crtbp_test->proc~compute_libration_points_v2

Source Code

    subroutine compute_libration_points_v2(mu,r1,r2,r3,r4,r5)

    use math_module, only: cube_root

    implicit none

    real(wp),intent(in)                        :: mu  !! CRTBP parameter
    real(wp),intent(out),optional              :: r1  !! L1 x coordinate
    real(wp),intent(out),optional              :: r2  !! L2 x coordinate
    real(wp),intent(out),optional              :: r3  !! L3 x coordinate
    real(wp),dimension(2),intent(out),optional :: r4  !! L4 [x,y] coordinates
    real(wp),dimension(2),intent(out),optional :: r5  !! L5 [x,y] coordinates

    integer,parameter  :: maxiter = 100    !! maximum number of iterations
    real(wp),parameter :: tol = 1.0e-12_wp !! convergence tolerance

    real(wp) :: gamma, gamma0
    integer :: i !! counter

    if (present(r1)) then
        gamma0 = cube_root(mu * (one-mu) / three)
        gamma = gamma0 + one
        do i = 1,maxiter
            if (abs(gamma-gamma0)<=tol) exit
            gamma0 = gamma
            gamma = cube_root((mu*(gamma0-one)**2)/(three-two*mu-gamma0*(three-mu-gamma0)))
        end do
        r1 = one - mu - gamma
    end if

    if (present(r2)) then
        gamma0 = cube_root(mu * (one-mu) / three)
        gamma = gamma0 + one
        do i = 1,maxiter
            if (abs(gamma-gamma0)<=tol) exit
            gamma0 = gamma
            gamma = cube_root((mu*(gamma0+one)**2)/(three-two*mu+gamma0*(three-mu+gamma0)))
        end do
        r2 = one - mu + gamma
    end if

    if (present(r3)) then
        gamma0 = cube_root(mu * (one-mu) / three)
        gamma = gamma0 + one
        do i = 1,maxiter
            if (abs(gamma-gamma0)<=tol) exit
            gamma0 = gamma
            gamma = cube_root((one-mu)*(gamma0+one)**2/(one+two*mu+gamma0*(two+mu+gamma0)))
        end do
        r3 = - mu - gamma
    end if

    call compute_libration_points(mu,r4=r4,r5=r5)

    end subroutine compute_libration_points_v2