This module contains various routines related to relative motion.

Axis systems

Three different axis systems are used here. They are:

The IJK frame
The LVLH frame, defined by:
- x-axis : completes the right handed system (for a perfectly-circular orbit, the x-axis is $\hat{\mathbf{v}}$ )
- y-axis : $-\hat{\mathbf{h}}$
- z-axis : $-\hat{\mathbf{r}}$
The RSW frame, defined by:
- x-axis : $\hat{\mathbf{r}}$
- y-axis : completes the right handed system (for a perfectly-circular orbit, the y-axis is $\hat{\mathbf{v}}$ )
- z-axis : $\hat{\mathbf{h}}$
The VUW frame, defined by:
- x-axis : $\hat{\mathbf{v}}$
- y-axis : completes the right handed system
- z-axis : $\hat{\mathbf{h}}$

Uses

- kind_module
- numbers_module
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Used by

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Interfaces

public interface from_ijk_to_lvlh

Conversion from IJK to LVLH

private subroutine from_ijk_to_lvlh_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert IJK to LVLH.

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_lvlh_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_lvlh, dv_lvlh, r_ijk, v_ijk)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from LVLH to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]

public interface from_ijk_to_rsw

Conversion from IJK to RSW

private subroutine from_ijk_to_rsw_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert IJK to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_ijk_to_rsw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_rsw, dv_rsw)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from IJK to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_rsw	Chaser RSW position vector relative to target [km]

public interface from_rsw_to_ijk

Conversion from RSW to IJK

private subroutine from_rsw_to_ijk_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert RSW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_rsw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_rsw, dv_rsw, r_ijk, v_ijk)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from RSW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_rsw	Chaser RSW position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_rsw	Chaser RSW velocity vector [km/s]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute velocity vector [km/s]

public interface from_lvlh_to_rsw

Conversion from LVLH to RSW

private subroutine from_lvlh_to_rsw_rv(dr_lvlh, dv_lvlh, dr_rsw, dv_rsw)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from LVLH to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_rsw	Chaser RSW velocity vector relative to target [km/s]

public interface from_rsw_to_lvlh

Conversion from RSW to LVLH

private subroutine from_rsw_to_lvlh_rv(dr_rsw, dv_rsw, dr_lvlh, dv_lvlh)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from RSW to LVLH.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_rsw	Chaser RSW velocity vector relative to target [km/s]
real(kind=wp),	intent(out),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]

public interface from_ijk_to_vuw

Conversion from IJK to vuw

private subroutine from_ijk_to_vuw_mat(mu, r, v, a, c, cdot)

Compute the transformation matrices to convert IJK to vuw.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2] this is used here to assume instantaneous conic motion if `a` is not present.
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_ijk_to_vuw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_vuw, dv_vuw)

Transform a position (and optionally velocity) vector from IJK to VUW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_vuw	Chaser vuw position vector relative to target [km]

public interface from_vuw_to_ijk

Conversion from vuw to IJK

private subroutine from_vuw_to_ijk_mat(mu, r, v, a, c, cdot)

Compute the transformation matrices to convert VUW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_vuw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_vuw, dv_vuw, r_ijk, v_ijk)

Transform a position (and optionally velocity) vector from VUW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]

Abstract Interfaces

abstract interface

private subroutine report_func(t, rv)

for reporting the points in the cw_propagator.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t	time [sec]
real(kind=wp),	intent(in),		dimension(6)	::	rv	state [km,km/s]

abstract interface

private subroutine frame_transform_func(mu, r, v, a, c, cdot)

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2] [not used by all algorithms]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

Functions

public function cw_equations(x0, dt, n) result(x)

Author: Jacob Williams
Date: 6/14/2015

Clohessy-Wiltshire equations for relative motion.

Arguments

Type	Intent	Attributes		Name
real(kind=wp),	intent(in),	dimension(6)	::	x0	initial state [r,v] of chaser (at t0) [km, km/s]
real(kind=wp),	intent(in)		::	dt	elapsed time from t0 [sec]
real(kind=wp),	intent(in)		::	n	mean motion of target orbit (`sqrt(mu/a**3)`) [1/sec]

Return Value real(kind=wp), dimension(6)

final state [r,v] of chaser [km, km/s]

Subroutines

public subroutine cw_propagator(t0, x0, h, n, tf, xf, report)

Author: Jacob Williams
Date: 8/23/2015

Clohessy-Wiltshire propagation routine.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	t0	initialize time [sec]
real(kind=wp),	intent(in),		dimension(6)	::	x0	initial state in RST coordinates [km,km/s]
real(kind=wp),	intent(in)			::	h	abs(time step) [sec]
real(kind=wp),	intent(in)			::	n	mean motion of target orbit (`sqrt(mu/a**3)`) [1/sec]
real(kind=wp),	intent(in)			::	tf	final time [sec]
real(kind=wp),	intent(out),		dimension(6)	::	xf	final state in RST coordinates [km,km/s]
procedure(report_func),		optional		::	report	to report each point

private subroutine from_ijk_to_frame_rv(mu, from_ijk_to_frame, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_frame, dv_frame)

Transform a position (and optionally velocity) vector from IJK to a specified relative frame.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
procedure(frame_transform_func)				::	from_ijk_to_frame	function to compute the transformation matrices
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_frame	Chaser frame position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_frame	Chaser frame position vector relative to target [km]

private subroutine from_frame_to_ijk_rv(mu, from_frame_to_ijk, rt_ijk, vt_ijk, dr_frame, dv_frame, r_ijk, v_ijk)

Transform a position (and optionally velocity) vector from a specified relative frame to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
procedure(frame_transform_func)				::	from_frame_to_ijk	function to compute the transformation matrices
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_frame	Chaser frame position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_frame	Chaser frame position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]

private subroutine from_ijk_to_lvlh_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert IJK to LVLH.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_ijk_to_lvlh_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_lvlh, dv_lvlh)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from IJK to LVLH.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]

private subroutine from_lvlh_to_ijk_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert LVLH to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_lvlh_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_lvlh, dv_lvlh, r_ijk, v_ijk)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from LVLH to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]

private subroutine from_ijk_to_vuw_mat(mu, r, v, a, c, cdot)

Compute the transformation matrices to convert IJK to vuw.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2] this is used here to assume instantaneous conic motion if `a` is not present.
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_ijk_to_vuw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_vuw, dv_vuw)

Transform a position (and optionally velocity) vector from IJK to VUW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_vuw	Chaser vuw position vector relative to target [km]

private subroutine from_vuw_to_ijk_mat(mu, r, v, a, c, cdot)

Compute the transformation matrices to convert VUW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_vuw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_vuw, dv_vuw, r_ijk, v_ijk)

Transform a position (and optionally velocity) vector from VUW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_vuw	Chaser vuw position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]

private subroutine from_ijk_to_rsw_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert IJK to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_ijk_to_rsw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_rsw, dv_rsw)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from IJK to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	v_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_rsw	Chaser RSW position vector relative to target [km]

private subroutine from_rsw_to_ijk_mat(mu, r, v, a, c, cdot)

Author: Jacob Williams
Date: 4/19/2014

Compute the transformation matrices to convert RSW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	r	position vector of target [km]
real(kind=wp),	intent(in),		dimension(3)	::	v	velocity vector of target [km/s]
real(kind=wp),	intent(in),	optional,	dimension(3)	::	a	acceleration vector of target [km/s^2] (if not present, then a torque-free force model is assumed)
real(kind=wp),	intent(out),		dimension(3,3)	::	c	C transformation matrix
real(kind=wp),	intent(out),	optional,	dimension(3,3)	::	cdot	CDOT transformation matrix

private subroutine from_rsw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_rsw, dv_rsw, r_ijk, v_ijk)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from RSW to IJK.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	mu	gravitational parameter [km^3/s^2]
real(kind=wp),	intent(in),		dimension(3)	::	rt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	vt_ijk	Target IJK absolute position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dr_rsw	Chaser RSW position vector [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_rsw	Chaser RSW velocity vector [km/s]
real(kind=wp),	intent(out),		dimension(3)	::	r_ijk	Chaser IJK absolute position vector [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	v_ijk	Chaser IJK absolute velocity vector [km/s]

private subroutine from_rsw_to_lvlh_rv(dr_rsw, dv_rsw, dr_lvlh, dv_lvlh)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from RSW to LVLH.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_rsw	Chaser RSW velocity vector relative to target [km/s]
real(kind=wp),	intent(out),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]

private subroutine from_lvlh_to_rsw_rv(dr_lvlh, dv_lvlh, dr_rsw, dv_rsw)

Author: Jacob Williams
Date: 8/23/2014

Transform a position (and optionally velocity) vector from LVLH to RSW.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in),		dimension(3)	::	dr_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(in),		dimension(3)	::	dv_lvlh	Chaser LVLH position vector relative to target [km]
real(kind=wp),	intent(out),		dimension(3)	::	dr_rsw	Chaser RSW position vector relative to target [km]
real(kind=wp),	intent(out),	optional,	dimension(3)	::	dv_rsw	Chaser RSW velocity vector relative to target [km/s]

public subroutine relative_motion_test()

Author: Jacob Williams
Date: 8/22/2015

Unit tests for the relative_motion_module.

Arguments

None

relative_motion_module Module

Contents

Interfaces

Abstract Interfaces

Functions

Subroutines

Axis systems

Uses

Used by

Interfaces

public interface from_ijk_to_lvlh

private subroutine from_ijk_to_lvlh_mat(mu, r, v, a, c, cdot)

See also

Arguments

private subroutine from_ijk_to_lvlh_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_lvlh, dv_lvlh)

Arguments

public interface from_lvlh_to_ijk

private subroutine from_lvlh_to_ijk_mat(mu, r, v, a, c, cdot)

See also

Arguments

private subroutine from_lvlh_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_lvlh, dv_lvlh, r_ijk, v_ijk)

Arguments

public interface from_ijk_to_rsw

private subroutine from_ijk_to_rsw_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_ijk_to_rsw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_rsw, dv_rsw)

Arguments

public interface from_rsw_to_ijk

private subroutine from_rsw_to_ijk_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_rsw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_rsw, dv_rsw, r_ijk, v_ijk)

Arguments

public interface from_lvlh_to_rsw

private subroutine from_lvlh_to_rsw_rv(dr_lvlh, dv_lvlh, dr_rsw, dv_rsw)

Arguments

public interface from_rsw_to_lvlh

private subroutine from_rsw_to_lvlh_rv(dr_rsw, dv_rsw, dr_lvlh, dv_lvlh)

Arguments

public interface from_ijk_to_vuw

private subroutine from_ijk_to_vuw_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_ijk_to_vuw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_vuw, dv_vuw)

Arguments

public interface from_vuw_to_ijk

private subroutine from_vuw_to_ijk_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_vuw_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_vuw, dv_vuw, r_ijk, v_ijk)

Arguments

Abstract Interfaces

abstract interface

private subroutine report_func(t, rv)

Arguments

abstract interface

private subroutine frame_transform_func(mu, r, v, a, c, cdot)

Arguments

Functions

public function cw_equations(x0, dt, n) result(x)

Arguments

Return Value real(kind=wp), dimension(6)

Subroutines

public subroutine cw_propagator(t0, x0, h, n, tf, xf, report)

Arguments

private subroutine from_ijk_to_frame_rv(mu, from_ijk_to_frame, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_frame, dv_frame)

Arguments

private subroutine from_frame_to_ijk_rv(mu, from_frame_to_ijk, rt_ijk, vt_ijk, dr_frame, dv_frame, r_ijk, v_ijk)

Arguments

private subroutine from_ijk_to_lvlh_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_ijk_to_lvlh_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_lvlh, dv_lvlh)

Arguments

private subroutine from_lvlh_to_ijk_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_lvlh_to_ijk_rv(mu, rt_ijk, vt_ijk, dr_lvlh, dv_lvlh, r_ijk, v_ijk)

Arguments

private subroutine from_ijk_to_vuw_mat(mu, r, v, a, c, cdot)

Arguments

private subroutine from_ijk_to_vuw_rv(mu, rt_ijk, vt_ijk, r_ijk, v_ijk, dr_vuw, dv_vuw)

Arguments

private subroutine from_vuw_to_ijk_mat(mu, r, v, a, c, cdot)

Arguments