transformation_module – fortran-astrodynamics-toolkit

Coordinate transformations.

Uses

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Used by

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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Variables

Type	Visibility	Attributes		Name		Initial
integer,	public,	parameter	::	center_at_primary_body	=	1
integer,	public,	parameter	::	center_at_secondary_body	=	2
integer,	public,	parameter	::	center_at_barycenter	=	3

Interfaces

public interface two_body_rotating_frame

private pure function two_body_rotating_frame_constructor(primary_body, secondary_body, center, et, inertial) result(f)

Constructor for a two_body_rotating_frame

Arguments

Type	Intent	Optional		Name
type(celestial_body),	intent(in)		::	primary_body	the primary body of the frame
type(celestial_body),	intent(in)		::	secondary_body	the secondary body used to construct the frame
integer,	intent(in)		::	center	the frame center (can be `primary_body`, `secondary_body`, or `barycenter`)
real(kind=wp),	intent(in)		::	et	epoch at which the frame is defined [sec]
logical,	intent(in),	optional	::	inertial	if true, it's a quasi-inertial frame [default is false]

Return Value type(two_body_rotating_frame)

public interface two_body_rotating_pulsating_frame

private pure function two_body_rotating_pulsating_frame_constructor(primary_body, secondary_body, center, scale, et) result(f)

Constructor for a two_body_rotating_pulsating_frame

Arguments

Type	Intent		Name
type(celestial_body),	intent(in)	::	primary_body	the primary body of the frame
type(celestial_body),	intent(in)	::	secondary_body	the secondary body used to construct the frame
integer,	intent(in)	::	center	the frame center (can be `primary_body`, `secondary_body`, or `barycenter`)
real(kind=wp),	intent(in)	::	scale	scale factor
real(kind=wp),	intent(in)	::	et	epoch at which the frame is defined [sec]

Return Value type(two_body_rotating_pulsating_frame)

public interface iau_earth_rotating_frame

private pure function iau_earth_rotating_frame_constructor(b, et) result(f)

Constructor for a iau_earth_rotating_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body
real(kind=wp),	intent(in)			::	et	epoch at which the frame is defined [sec]

Return Value type(iau_earth_rotating_frame)

public interface iau_moon_rotating_frame

private pure function iau_moon_rotating_frame_constructor(b, et) result(f)

Constructor for a iau_moon_rotating_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body
real(kind=wp),	intent(in)			::	et	epoch at which the frame is defined [sec]

Return Value type(iau_earth_rotating_frame)

public interface icrf_frame

private pure function icrf_frame_constructor(b) result(f)

Constructor for a icrf_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body

Return Value type(icrf_frame)

public interface ecliptic_frame

private pure function ecliptic_frame_constructor(b) result(f)

Constructor for a ecliptic_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body

Return Value type(ecliptic_frame)

Abstract Interfaces

abstract interface

private subroutine c_cdot_func(me, eph, to_icrf, c, cdot, status_ok)

Arguments

Type	Intent	Optional	Attributes		Name
class(reference_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

Derived Types

type, public, abstract :: reference_frame

a reference frame defines an orientation at a specified frame center at a specified epoch. Usually, the center is the primary_body of the frame, but can be otherwise for a two_body_rotating_frame.

Components

Type	Visibility	Attributes		Name		Initial
type(celestial_body),	private		::	primary_body	=	body_earth	the primary body of the frame
real(kind=wp),	private		::	et	=	zero	epoch at which the frame is defined [sec]

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure(c_cdot_func), private, deferred :: get_c_cdot	to get the rotating matrix for the frame orientation

type, public, abstract, extends(reference_frame) :: inertial_frame_class

a non-rotating frame (a frame where the orientation axes are time invariant)

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine

type, public, abstract, extends(reference_frame) :: rotating_frame_class

a rotating frame (a frame where the orientation axes vary with time)

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine

type, public, abstract, extends(rotating_frame_class) :: iau_rotating_frame_class

frame defined by the orientation of a celestial body using the IAU models.

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine

type, public, extends(rotating_frame_class) :: two_body_rotating_frame

The two-body rotating frame is constructed from the states of two celestial bodies.

Components

Type	Visibility	Attributes		Name		Initial
type(celestial_body),	public		::	secondary_body	=	body_moon	the secondary body used to construct the frame
integer,	public		::	center	=	center_at_barycenter	the frame center (can be primary_body,secondary_body, or barycenter)
real(kind=wp),	public,	dimension(6)	::	rv12	=	zero	[r,v] of secondary body w.r.t. primary body
logical,	public		::	inertial	=	.false.	to make it a quasi-inertial frame (cdot is zero)

Constructor

private pure function two_body_rotating_frame_constructor (primary_body, secondary_body, center, et, inertial)	Constructor for a two_body_rotating_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: from_primary_to_center
procedure, public :: get_c_cdot => get_c_cdot_two_body_rotating

type, public, extends(two_body_rotating_frame) :: two_body_rotating_pulsating_frame

This frame is an extension of the two-body rotating frame, where a scale factor is used to scale the position and velocity of the state based on the distance between the primary and secondary bodies.

Components

Type	Visibility	Attributes		Name		Initial
type(celestial_body),	public		::	secondary_body	=	body_moon	the secondary body used to construct the frame
integer,	public		::	center	=	center_at_barycenter	the frame center (can be primary_body,secondary_body, or barycenter)
real(kind=wp),	public,	dimension(6)	::	rv12	=	zero	[r,v] of secondary body w.r.t. primary body
logical,	public		::	inertial	=	.false.	to make it a quasi-inertial frame (cdot is zero)
real(kind=wp),	public		::	scale	=	zero	scale factor

Constructor

private pure function two_body_rotating_pulsating_frame_constructor (primary_body, secondary_body, center, scale, et)	Constructor for a two_body_rotating_pulsating_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: from_primary_to_center
procedure, public :: get_c_cdot => get_c_cdot_two_body_rotating_pulsating

type, public, extends(iau_rotating_frame_class) :: iau_earth_rotating_frame

IAU Earth frame

Constructor

private pure function iau_earth_rotating_frame_constructor (b, et)	Constructor for a iau_earth_rotating_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: get_c_cdot => get_c_cdot_iau_earth

type, public, extends(iau_rotating_frame_class) :: iau_moon_rotating_frame

IAU Moon frame

Constructor

private pure function iau_moon_rotating_frame_constructor (b, et)	Constructor for a iau_moon_rotating_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: get_c_cdot => get_c_cdot_iau_moon

type, public, extends(inertial_frame_class) :: icrf_frame

the fundamental inertial frame for the ephemeris (i.e., J2000).

Constructor

private pure function icrf_frame_constructor (b)	Constructor for a icrf_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: get_c_cdot => get_c_cdot_icrf

type, public, extends(inertial_frame_class) :: ecliptic_frame

Mean ecliptic frame.

Constructor

private pure function ecliptic_frame_constructor (b)	Constructor for a ecliptic_frame

Type-Bound Procedures

procedure, public, pass(from) :: transform	coordinate transformation routine
procedure, public :: get_c_cdot => get_c_cdot_ecliptic

Functions

private pure function two_body_rotating_frame_constructor(primary_body, secondary_body, center, et, inertial) result(f)

Constructor for a two_body_rotating_frame

Arguments

Type	Intent	Optional		Name
type(celestial_body),	intent(in)		::	primary_body	the primary body of the frame
type(celestial_body),	intent(in)		::	secondary_body	the secondary body used to construct the frame
integer,	intent(in)		::	center	the frame center (can be `primary_body`, `secondary_body`, or `barycenter`)
real(kind=wp),	intent(in)		::	et	epoch at which the frame is defined [sec]
logical,	intent(in),	optional	::	inertial	if true, it's a quasi-inertial frame [default is false]

Return Value type(two_body_rotating_frame)

private pure function two_body_rotating_pulsating_frame_constructor(primary_body, secondary_body, center, scale, et) result(f)

Constructor for a two_body_rotating_pulsating_frame

Arguments

Type	Intent		Name
type(celestial_body),	intent(in)	::	primary_body	the primary body of the frame
type(celestial_body),	intent(in)	::	secondary_body	the secondary body used to construct the frame
integer,	intent(in)	::	center	the frame center (can be `primary_body`, `secondary_body`, or `barycenter`)
real(kind=wp),	intent(in)	::	scale	scale factor
real(kind=wp),	intent(in)	::	et	epoch at which the frame is defined [sec]

Return Value type(two_body_rotating_pulsating_frame)

private pure function iau_earth_rotating_frame_constructor(b, et) result(f)

Constructor for a iau_earth_rotating_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body
real(kind=wp),	intent(in)			::	et	epoch at which the frame is defined [sec]

Return Value type(iau_earth_rotating_frame)

private pure function iau_moon_rotating_frame_constructor(b, et) result(f)

Constructor for a iau_moon_rotating_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body
real(kind=wp),	intent(in)			::	et	epoch at which the frame is defined [sec]

Return Value type(iau_earth_rotating_frame)

private pure function icrf_frame_constructor(b) result(f)

Constructor for a icrf_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body

Return Value type(icrf_frame)

private pure function ecliptic_frame_constructor(b) result(f)

Constructor for a ecliptic_frame

Arguments

Type	Intent	Optional	Attributes		Name
type(celestial_body),	intent(in)			::	b	the central body

Return Value type(ecliptic_frame)

Subroutines

private subroutine transform(from, rv, to, et, eph, rv_out, status_ok)

Transform a Cartesian state from one reference frame to another at a specified epoch. The from and to reference_frames may each be defined at a different epoch. The et ephemeris time is the time the transformation is to be done, and accounts for the motion of the two frame centers from from%et and to%et to et.

Arguments

Type	Intent	Attributes		Name
class(reference_frame),	intent(inout)		::	from
real(kind=wp),	intent(in),	dimension(6)	::	rv
class(reference_frame),	intent(inout)		::	to
real(kind=wp),	intent(in)		::	et	the time of the transformation [sec]
class(ephemeris_class),	intent(inout)		::	eph	for ephemeris computations (assumed to have already been initialized)
real(kind=wp),	intent(out),	dimension(6)	::	rv_out
logical,	intent(out)		::	status_ok

private subroutine rvcto_rvcfrom_icrf(from, to, eph, et, rc21, vc21, status_ok)

Returns the state of the from frame center w.r.t. the to frame center, at the specified ephemeris time et.

Arguments

Type	Intent	Attributes		Name
class(reference_frame),	intent(in)		::	from
class(reference_frame),	intent(in)		::	to
class(ephemeris_class),	intent(inout)		::	eph	for ephemeris computations (assumed to have already been initialized)
real(kind=wp),	intent(in)		::	et	ephemeris time [sec]
real(kind=wp),	intent(out),	dimension(3)	::	rc21	position of `from` frame center w.r.t. `to` frame center
real(kind=wp),	intent(out),	dimension(3)	::	vc21	velocity of `from` frame center w.r.t. `to` frame center
logical,	intent(out)		::	status_ok	true if there were no errors

private subroutine from_primary_to_center(me, eph, et, rc, status_ok)

returns the state of the frame center w.r.t. the frame primary body.

Arguments

Type	Intent	Attributes		Name
class(two_body_rotating_frame),	intent(in)		::	me
class(ephemeris_class),	intent(inout)		::	eph	for ephemeris computations (assumed to have already been initialized)
real(kind=wp),	intent(in)		::	et	ephemeris time [sec]
real(kind=wp),	intent(out),	dimension(6)	::	rc	state of frame center w.r.t. primary body [inertial]
logical,	intent(out)		::	status_ok	true if no errors.

private subroutine get_c_cdot_two_body_rotating(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for ROTATING <-> ICRF

Arguments

Type	Intent	Optional	Attributes		Name
class(two_body_rotating_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

private subroutine get_c_cdot_two_body_rotating_pulsating(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for ROTATING_PULSATING <-> ICRF

Arguments

Type	Intent	Optional	Attributes		Name
class(two_body_rotating_pulsating_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

private subroutine get_c_cdot_icrf(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for ICRF <-> ICRF

Arguments

Type	Intent	Optional	Attributes		Name
class(icrf_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

private subroutine get_c_cdot_ecliptic(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for ICRF <-> Mean Ecliptic

Arguments

Type	Intent	Optional	Attributes		Name
class(ecliptic_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

private subroutine get_c_cdot_iau_earth(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for IAU_EARTH <-> ICRF

Arguments

Type	Intent	Optional	Attributes		Name
class(iau_earth_rotating_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

private subroutine get_c_cdot_iau_moon(me, eph, to_icrf, c, cdot, status_ok)

rotation matrix for IAU_MOON <-> ICRF

Arguments

Type	Intent	Optional	Attributes		Name
class(iau_moon_rotating_frame),	intent(inout)			::	me
class(ephemeris_class),	intent(inout)			::	eph	for ephemeris computations (assumed to have already been initialized)
logical,	intent(in)			::	to_icrf
real(kind=wp),	intent(out),		dimension(3,3)	::	c
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot
logical,	intent(out)			::	status_ok

public subroutine transformation_module_test()

Transformation units test

Arguments

None

transformation_module Module

Contents

Variables

Interfaces

Abstract Interfaces

Derived Types

Functions

Subroutines

Uses

Used by

Variables

Interfaces

public interface two_body_rotating_frame

private pure function two_body_rotating_frame_constructor(primary_body, secondary_body, center, et, inertial) result(f)

Arguments

Return Value type(two_body_rotating_frame)

public interface two_body_rotating_pulsating_frame

private pure function two_body_rotating_pulsating_frame_constructor(primary_body, secondary_body, center, scale, et) result(f)

Arguments

Return Value type(two_body_rotating_pulsating_frame)

public interface iau_earth_rotating_frame

private pure function iau_earth_rotating_frame_constructor(b, et) result(f)

Arguments

Return Value type(iau_earth_rotating_frame)

public interface iau_moon_rotating_frame

private pure function iau_moon_rotating_frame_constructor(b, et) result(f)

Arguments

Return Value type(iau_earth_rotating_frame)

public interface icrf_frame

private pure function icrf_frame_constructor(b) result(f)

Arguments

Return Value type(icrf_frame)

public interface ecliptic_frame

private pure function ecliptic_frame_constructor(b) result(f)

Arguments

Return Value type(ecliptic_frame)

Abstract Interfaces

abstract interface

private subroutine c_cdot_func(me, eph, to_icrf, c, cdot, status_ok)

Arguments

Derived Types

type, public, abstract :: reference_frame

Components

Type-Bound Procedures

type, public, abstract, extends(reference_frame) :: inertial_frame_class

Type-Bound Procedures

type, public, abstract, extends(reference_frame) :: rotating_frame_class

Type-Bound Procedures

type, public, abstract, extends(rotating_frame_class) :: iau_rotating_frame_class

Type-Bound Procedures

type, public, extends(rotating_frame_class) :: two_body_rotating_frame

Components

Constructor

Type-Bound Procedures

type, public, extends(two_body_rotating_frame) :: two_body_rotating_pulsating_frame

Components

Constructor

Type-Bound Procedures

type, public, extends(iau_rotating_frame_class) :: iau_earth_rotating_frame

Constructor

Type-Bound Procedures

type, public, extends(iau_rotating_frame_class) :: iau_moon_rotating_frame

Constructor

Type-Bound Procedures

type, public, extends(inertial_frame_class) :: icrf_frame

Constructor

Type-Bound Procedures

type, public, extends(inertial_frame_class) :: ecliptic_frame

Constructor

Type-Bound Procedures

Functions

private pure function two_body_rotating_frame_constructor(primary_body, secondary_body, center, et, inertial) result(f)

Arguments

Return Value type(two_body_rotating_frame)

private pure function two_body_rotating_pulsating_frame_constructor(primary_body, secondary_body, center, scale, et) result(f)

Arguments

Return Value type(two_body_rotating_pulsating_frame)

private pure function iau_earth_rotating_frame_constructor(b, et) result(f)

Arguments

Return Value type(iau_earth_rotating_frame)