laplace_coefficients Module

Module containing the functions used to compute lpalace coefficients and their derivatives.


Uses

  • module~~laplace_coefficients~~UsesGraph module~laplace_coefficients laplace_coefficients ieee_exceptions ieee_exceptions module~laplace_coefficients->ieee_exceptions module~globals globals module~laplace_coefficients->module~globals iso_c_binding iso_c_binding module~globals->iso_c_binding iso_fortran_env iso_fortran_env module~globals->iso_fortran_env

Used by

  • module~~laplace_coefficients~~UsedByGraph module~laplace_coefficients laplace_coefficients module~swiftest swiftest module~swiftest->module~laplace_coefficients module~bindings_module bindings_module module~bindings_module->module~swiftest module~dust dust module~dust->module~swiftest module~helio helio module~dust->module~helio module~symba symba module~dust->module~symba module~whm whm module~dust->module~whm module~fraggle fraggle module~fraggle->module~swiftest module~helio->module~swiftest module~helio->module~whm module~ringmoons ringmoons module~ringmoons->module~swiftest module~ringmoons->module~symba module~rmvs rmvs module~rmvs->module~swiftest module~rmvs->module~whm module~s_coarray_clone s_coarray_clone module~s_coarray_clone->module~swiftest module~s_coarray_collect s_coarray_collect module~s_coarray_collect->module~swiftest module~s_collision_check s_collision_check module~s_collision_check->module~swiftest module~s_collision_check->module~symba module~s_collision_generate s_collision_generate module~s_collision_generate->module~swiftest module~s_collision_io s_collision_io module~s_collision_io->module~swiftest module~s_collision_regime s_collision_regime module~s_collision_regime->module~swiftest module~s_collision_resolve s_collision_resolve module~s_collision_resolve->module~swiftest module~s_collision_util s_collision_util module~s_collision_util->module~swiftest module~s_encounter_check s_encounter_check module~s_encounter_check->module~swiftest module~s_encounter_io s_encounter_io module~s_encounter_io->module~swiftest module~s_encounter_util s_encounter_util module~s_encounter_util->module~swiftest module~s_fraggle_generate s_fraggle_generate module~s_fraggle_generate->module~swiftest module~s_fraggle_generate->module~fraggle module~s_fraggle_generate->module~symba module~s_fraggle_util s_fraggle_util module~s_fraggle_util->module~swiftest module~s_fraggle_util->module~fraggle module~s_helio_drift s_helio_drift module~s_helio_drift->module~swiftest module~s_helio_drift->module~helio module~s_helio_gr s_helio_gr module~s_helio_gr->module~swiftest module~s_helio_gr->module~helio module~s_helio_kick s_helio_kick module~s_helio_kick->module~swiftest module~s_helio_kick->module~helio module~s_helio_step s_helio_step module~s_helio_step->module~swiftest module~s_helio_step->module~helio module~s_helio_util s_helio_util module~s_helio_util->module~swiftest module~s_helio_util->module~helio module~s_operator_cross s_operator_cross module~s_operator_cross->module~swiftest module~s_ringmoons_io s_ringmoons_io module~s_ringmoons_io->module~swiftest module~s_ringmoons_io->module~ringmoons module~s_ringmoons_step s_ringmoons_step module~s_ringmoons_step->module~swiftest module~s_ringmoons_step->module~ringmoons module~s_ringmoons_torque s_ringmoons_torque module~s_ringmoons_torque->module~swiftest module~s_ringmoons_torque->module~ringmoons module~s_ringmoons_util s_ringmoons_util module~s_ringmoons_util->module~swiftest module~s_ringmoons_util->module~ringmoons module~s_rmvs_discard s_rmvs_discard module~s_rmvs_discard->module~swiftest module~s_rmvs_discard->module~rmvs module~s_rmvs_encounter_check s_rmvs_encounter_check module~s_rmvs_encounter_check->module~swiftest module~s_rmvs_encounter_check->module~rmvs module~s_rmvs_kick s_rmvs_kick module~s_rmvs_kick->module~swiftest module~s_rmvs_kick->module~rmvs module~s_rmvs_step s_rmvs_step module~s_rmvs_step->module~swiftest module~s_rmvs_step->module~rmvs module~shgrav shgrav module~s_rmvs_step->module~shgrav module~s_rmvs_util s_rmvs_util module~s_rmvs_util->module~swiftest module~s_rmvs_util->module~rmvs module~s_shgrav_accel s_shgrav_accel module~s_shgrav_accel->module~swiftest module~s_shgrav_accel->module~shgrav module~s_shgrav_pot s_shgrav_pot module~s_shgrav_pot->module~swiftest module~s_shgrav_pot->module~shgrav module~s_swiftest_coarray s_swiftest_coarray module~s_swiftest_coarray->module~swiftest module~s_swiftest_discard s_swiftest_discard module~s_swiftest_discard->module~swiftest module~s_swiftest_drift s_swiftest_drift module~s_swiftest_drift->module~swiftest module~s_swiftest_driver s_swiftest_driver module~s_swiftest_driver->module~swiftest module~s_swiftest_gr s_swiftest_gr module~s_swiftest_gr->module~swiftest module~s_swiftest_io s_swiftest_io module~s_swiftest_io->module~swiftest module~s_swiftest_io->module~ringmoons module~s_swiftest_io->module~symba module~s_swiftest_kick s_swiftest_kick module~s_swiftest_kick->module~swiftest module~s_swiftest_obl s_swiftest_obl module~s_swiftest_obl->module~swiftest module~s_swiftest_obl->module~shgrav module~s_swiftest_orbel s_swiftest_orbel module~s_swiftest_orbel->module~swiftest module~s_swiftest_radiation s_swiftest_radiation module~s_swiftest_radiation->module~swiftest module~s_swiftest_user s_swiftest_user module~s_swiftest_user->module~swiftest module~s_swiftest_util s_swiftest_util module~s_swiftest_util->module~swiftest module~s_swiftest_util->module~fraggle module~s_swiftest_util->module~helio module~s_swiftest_util->module~ringmoons module~s_swiftest_util->module~rmvs module~s_swiftest_util->module~symba module~s_swiftest_util->module~whm module~s_symba_discard s_symba_discard module~s_symba_discard->module~swiftest module~s_symba_discard->module~symba module~s_symba_drift s_symba_drift module~s_symba_drift->module~swiftest module~s_symba_drift->module~symba module~s_symba_encounter_check s_symba_encounter_check module~s_symba_encounter_check->module~swiftest module~s_symba_encounter_check->module~symba module~s_symba_gr s_symba_gr module~s_symba_gr->module~swiftest module~s_symba_gr->module~symba module~s_symba_kick s_symba_kick module~s_symba_kick->module~swiftest module~s_symba_kick->module~symba module~s_symba_step s_symba_step module~s_symba_step->module~swiftest module~s_symba_step->module~symba module~s_symba_util s_symba_util module~s_symba_util->module~swiftest module~s_symba_util->module~fraggle module~s_symba_util->module~symba module~s_tides_kick_getacch s_tides_kick_getacch module~s_tides_kick_getacch->module~swiftest module~s_tides_step_rot s_tides_step_rot module~s_tides_step_rot->module~swiftest module~s_walltime s_walltime module~s_walltime->module~swiftest module~s_whm_coord s_whm_coord module~s_whm_coord->module~swiftest module~s_whm_coord->module~whm module~s_whm_gr s_whm_gr module~s_whm_gr->module~swiftest module~s_whm_gr->module~whm module~s_whm_kick s_whm_kick module~s_whm_kick->module~swiftest module~s_whm_kick->module~whm module~s_whm_step s_whm_step module~s_whm_step->module~swiftest module~s_whm_step->module~whm module~s_whm_util s_whm_util module~s_whm_util->module~swiftest module~s_whm_util->module~whm module~shgrav->module~swiftest module~symba->module~swiftest module~symba->module~helio module~whm->module~swiftest module~whm_drift whm_drift module~whm_drift->module~swiftest module~whm_drift->module~whm program~main main program~main->module~swiftest

Functions

public pure recursive function compute_laplace_coefficient(alpha, j, s, n) result(ans)

Author
David A. Minton

Computes the Laplace coefficient b_s^(j)(alpha) and its derivatives using the recursive relations given in Murray & Dermott (1999), including the case where alpha is close to 1 where the G(y) series solution is used.

Arguments

Type IntentOptional Attributes Name
real(kind=DP), intent(in) :: alpha

alpha is the ratio of the inner to outer semimajor axis (a_inner/a_outer) for the coefficient being computed
integer(kind=I4B), intent(in) :: j

j is the index of the Laplace coefficient being computed.
real(kind=DP), intent(in) :: s

s is the order of the Laplace coefficient being computed.

integer(kind=I4B), intent(in) :: n

n is the order of the derivative. n=0 gives the coefficient itself, n=1 gives the first derivative, etc.

Return Value real(kind=DP)

The value of the Laplace coefficient or its derivative, depending on n.