compute_monodromy_matrix_eigenvalues Subroutine

public subroutine compute_monodromy_matrix_eigenvalues(phi, lambda)

Uses

  • proc~~compute_monodromy_matrix_eigenvalues~~UsesGraph proc~compute_monodromy_matrix_eigenvalues halo_orbit_module::compute_monodromy_matrix_eigenvalues module~matrix_module matrix_module proc~compute_monodromy_matrix_eigenvalues->module~matrix_module module~kind_module kind_module module~matrix_module->module~kind_module module~numbers_module numbers_module module~matrix_module->module~numbers_module iso_fortran_env iso_fortran_env module~kind_module->iso_fortran_env module~numbers_module->module~kind_module

Compute the eigenvalues of the monodromy matrix.

Reference

  • J.S. Parker, R.L. Anderson, "Low-Energy Lunar Trajectory Design",
    1. (p 79)

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in), dimension(6,6) :: phi

monodromy matrix
complex(kind=wp), intent(out), dimension(6) :: lambda

eigenvalues of phi

Calls

proc~~compute_monodromy_matrix_eigenvalues~~CallsGraph proc~compute_monodromy_matrix_eigenvalues halo_orbit_module::compute_monodromy_matrix_eigenvalues proc~matrix_trace matrix_module::matrix_trace proc~compute_monodromy_matrix_eigenvalues->proc~matrix_trace

Source Code

    subroutine compute_monodromy_matrix_eigenvalues(phi,lambda)

    use matrix_module, only: matrix_trace

    implicit none

    real(wp),dimension(6,6),intent(in)   :: phi    !! monodromy matrix
    complex(wp),dimension(6),intent(out) :: lambda !! eigenvalues of `phi`

    real(wp) :: alpha, beta, alpha2
    complex(wp) :: p, q, a, b, c

    alpha  = two - matrix_trace(6,phi)
    alpha2 = alpha*alpha
    beta   = (alpha2 - matrix_trace(6,matmul(phi,phi)))/two + one
    a      = sqrt(alpha2 - four*beta + eight)
    p      = (alpha + a) / two
    q      = (alpha - a) / two
    b      = sqrt(p*p - four)
    c      = sqrt(q*q - four)

    ! eigenvalues:
    lambda(1) = (-p + b) / two
    lambda(2) = (-p - b) / two
    lambda(3) = (-q + c) / two
    lambda(4) = (-q - c) / two
    lambda(5) = (one, zero)
    lambda(6) = (one, zero)

    end subroutine compute_monodromy_matrix_eigenvalues