crtbp_module – fortran-astrodynamics-toolkit

This module contains various routines related to the Circular Restricted Three-Body Problem (CRTBP).

Uses

- numbers_module
- kind_module
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Used by

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Functions

public pure function compute_crtpb_parameter(mu1, mu2) result(mu)

Compute $\mu$ , the normalized CRTBP parameter. It is equal to $M_2 / (M_1 + M_2)$ .

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu1	grav param for body 1 $[km^3/s^2]$
real(kind=wp),	intent(in)			::	mu2	grav param for body 2 $[km^3/s^2]$

Return Value real(kind=wp)

CRTBP parameter $\mu$

public pure function compute_jacobi_constant(mu, x) result(c)

Compute the CRTBP Jacobi constant, given the state.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	CRTBP parameter (See compute_crtpb_parameter)
real(kind=wp),	intent(in),		dimension(6)	::	x	normalized state vector

Return Value real(kind=wp)

Jacobi constant

Subroutines

public subroutine normalize_variables(mu1, mu2, d12, x, m, t, x_crtbp, m_crtbp, t_crtbp)

Convert state in km, km/s units to normalized CRTBP state.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu1	grav. param. of body 1 $[\mathrm{km}^3/\mathrm{s}^2]$
real(kind=wp),	intent(in)			::	mu2	grav. param. of body 2 $[\mathrm{km}^3/\mathrm{s}^2]$
real(kind=wp),	intent(in)			::	d12	distance between body 1 and body 2 [km]
real(kind=wp),	intent(in),	optional,	dimension(6)	::	x	unnormalized state w.r.t. barycenter [km,km/s]
real(kind=wp),	intent(in),	optional		::	m	unnormalized mass [kg]
real(kind=wp),	intent(in),	optional		::	t	unnormalized time [sec]
real(kind=wp),	intent(out),	optional,	dimension(6)	::	x_crtbp	CRTBP normalized state
real(kind=wp),	intent(out),	optional		::	m_crtbp	CRTBP normalized mass
real(kind=wp),	intent(out),	optional		::	t_crtbp	CRTBP normalized time

public subroutine unnormalize_variables(mu1, mu2, d12, x_crtbp, m_crtbp, t_crtbp, x, m, t)

Convert normalized CRTBP state to km, km/s units.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu1	grav. param. of body 1 $[\mathrm{km}^3/\mathrm{s}^2]$
real(kind=wp),	intent(in)			::	mu2	grav. param. of body 2 $[\mathrm{km}^3/\mathrm{s}^2]$
real(kind=wp),	intent(in)			::	d12	distance between body 1 and body 2 [km]
real(kind=wp),	intent(in),	optional,	dimension(6)	::	x_crtbp	CRTBP normalized state
real(kind=wp),	intent(in),	optional		::	m_crtbp	CRTBP normalized mass
real(kind=wp),	intent(in),	optional		::	t_crtbp	CRTBP normalized time
real(kind=wp),	intent(out),	optional,	dimension(6)	::	x	unnormalized state w.r.t. barycenter [km,km/s]
real(kind=wp),	intent(out),	optional		::	m	unnormalized mass [kg]
real(kind=wp),	intent(out),	optional		::	t	unnormalized time [sec]

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

Compute the coordinates of the libration points (L1,L2,L3,L4,L5). L1-L3 are computed using Newton's method. L4-L5 are known analytically.

Arguments

Type	Intent	Optional	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

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

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

Arguments

Type	Intent	Optional	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

public subroutine crtbp_derivs(mu, x, dx)

CRTBP derivatives: state only.

Arguments

Type	Intent	Attributes		Name
real(kind=wp),	intent(in)		::	mu	CRTBP parameter (See compute_crtpb_parameter)
real(kind=wp),	intent(in),	dimension(6)	::	x	normalized state $[\mathbf{r},\mathbf{v}]$
real(kind=wp),	intent(out),	dimension(6)	::	dx	normalized state derivative $[\dot{\mathbf{r}},\dot{\mathbf{v}}]$

public subroutine crtbp_derivs_with_stm(mu, x, dx)

CRTBP derivatives: state + state transition matrix.

Arguments

Type	Intent	Attributes		Name
real(kind=wp),	intent(in)		::	mu	CRTBP parameter (See compute_crtpb_parameter)
real(kind=wp),	intent(in),	dimension(42)	::	x	normalized state and STM $[\mathbf{r},\mathbf{v},\mathbf{\Phi}]$
real(kind=wp),	intent(out),	dimension(42)	::	dx	normalized state and STM derivative $[\dot{\mathbf{r}},\dot{\mathbf{v}},\dot{\mathbf{\Phi}}]$

public subroutine crtbp_test()

Unit tests for CRTBP routines.

Arguments

None

crtbp_module Module

Contents

Functions

Subroutines

Uses

Used by

Functions

public pure function compute_crtpb_parameter(mu1, mu2) result(mu)

Arguments

Return Value real(kind=wp)

public pure function compute_jacobi_constant(mu, x) result(c)

Arguments

Return Value real(kind=wp)

Subroutines

public subroutine normalize_variables(mu1, mu2, d12, x, m, t, x_crtbp, m_crtbp, t_crtbp)

Arguments

public subroutine unnormalize_variables(mu1, mu2, d12, x_crtbp, m_crtbp, t_crtbp, x, m, t)

Arguments

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

Arguments

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

Arguments

public subroutine crtbp_derivs(mu, x, dx)

Arguments

public subroutine crtbp_derivs_with_stm(mu, x, dx)

Arguments

public subroutine crtbp_test()

Arguments