Struct container for the (modified) equinoctial orbital elements. More...

#include <OrbitalElements.hh>

Public Member Functions
	Equinoctial ()
	Equinoctial (Real const t_p, Real const t_f, Real const t_g, Real const t_h, Real const t_k)
	Equinoctial (Vector5 const &t_equi)
	Equinoctial (Equinoctial const &)=default
	Equinoctial (Equinoctial &&)=default
Equinoctial &	operator= (const Equinoctial &)=default
Equinoctial &	operator= (Equinoctial &&)=default
Vector5	vector () const
std::string	info () const
void	info (std::ostream &os)
void	reset ()
bool	sanity_check () const
bool	is_singular (Real tol_i=EPSILON_LOW) const
bool	is_nonsingular (Real tol_i=EPSILON_LOW) const
Real	u (Real L) const
Real	a () const
Real	e () const
Real	i () const
Real	omega () const
Real	Omega () const

Public Attributes
Real	p {QUIET_NAN}
Real	f {QUIET_NAN}
Real	g {QUIET_NAN}
Real	h {QUIET_NAN}
Real	k {QUIET_NAN}

Detailed Description

The (modified) equinoctial orbital elements are defined as follows:

the semi-latus rectum \( p \) (UA).
the \( x \)-axis component of the eccentricity vector in the orbital frame \( f \) (-).
the \( y \)-axis component of the eccentricity vector in the orbital frame \( g \) (-).
the \( x \)-axis component of the node vector in the orbital frame \( h \) (-).
the \( y \)-axis component of the node vector in the orbital frame \( k \) (-).
the posigrade (+1)/retrograde (-1) factor \( I = +1 \) (posigrade) or \( I = -1 \) (retrograde) (-). Singular at \( i = \pi \).

Note: For more information on orbital elements, refer to "Survey of Orbital Elements", by G. R. Hintz, Journal of Guidance, Control, and Dynamics, Vol. 31, No. 3, May-June 2008.

Constructor & Destructor Documentation

◆ Equinoctial() [1/5]

Astro::OrbitalElements::Equinoctial::Equinoctial ( )

inline

Struct constructor for the (modified) equinoctial orbit parameters.

◆ Equinoctial() [2/5]

Astro::OrbitalElements::Equinoctial::Equinoctial	(	Real const	t_p,
		Real const	t_f,
		Real const	t_g,
		Real const	t_h,
		Real const	t_k )

inline

Struct constructor for the (modified) equinoctial orbit parameters.

Parameters

[in]	t_p	The semi-latus rectum \( p \).
[in]	t_f	The \( x \)-axis component of the eccentricity vector in the orbital frame.
[in]	t_g	The \( y \)-axis component of the eccentricity vector in the orbital frame.
[in]	t_h	The \( x \)-axis component of the node vector in the orbital frame.
[in]	t_k	The \( y \)-axis component of the node vector in the orbital frame.

◆ Equinoctial() [3/5]

Astro::OrbitalElements::Equinoctial::Equinoctial ( Vector5 const & t_equi )

inline

Struct constructor for the (modified) equinoctial orbit parameters.

Parameters

[in] t_equi The vector of equinoctial orbit parameters \( [p, f, g, h, k]^\top \).

Note: The vector \( t_{\text{equinoctial}} \) must have 5 elements.

◆ Equinoctial() [4/5]

Astro::OrbitalElements::Equinoctial::Equinoctial ( Equinoctial const & )

default

Enable the default equinoctial orbit parameters copy constructor.

◆ Equinoctial() [5/5]

Astro::OrbitalElements::Equinoctial::Equinoctial ( Equinoctial && )

default

Enable the default equinoctial orbit parameters move constructor.

Member Function Documentation

◆ a()

Real Astro::OrbitalElements::Equinoctial::a ( ) const

inline

Compute the semi-major axis \( a = \displaystyle\frac{p}{1 - f^2 - g^2} \) (UA).

Returns: The semi-major axis \( a \).

◆ e()

Real Astro::OrbitalElements::Equinoctial::e ( ) const

inline

Compute the eccentricity \( \mathbf{e} = [f, g, 0]^\top \) (-).

Returns: The eccentricity \( \mathbf{e} \).

◆ i()

Real Astro::OrbitalElements::Equinoctial::i ( ) const

inline

Compute the inclination \( i = \arctan\left(2\sqrt{h^2 + k^2}, 1 - h^2 - k^2\right) \) (rad).

Returns: The inclination \( i \).

◆ info() [1/2]

std::string Astro::OrbitalElements::Equinoctial::info ( ) const

inline

Print the equinoctial orbit parameters on a string.

Returns: Equinoctial orbit parameters string.

◆ info() [2/2]

void Astro::OrbitalElements::Equinoctial::info ( std::ostream & os )

inline

Print the equinoctial orbit parameters on a stream.

Parameters

[in,out] os Output stream.

◆ is_nonsingular()

bool Astro::OrbitalElements::Equinoctial::is_nonsingular ( Real tol_i = EPSILON_LOW ) const

inline

Check if the equinoctial orbit is singular, i.e., * \( \pi-\varepsilon_i < i < \pi+\varepsilon_i\).

Parameters

[in] tol_i Tolerance \( \varepsilon_i \) for the singularity check on the inclination.

Returns: True if the equinoctial orbit is nonsingular, false otherwise.

◆ is_singular()

bool Astro::OrbitalElements::Equinoctial::is_singular ( Real tol_i = EPSILON_LOW ) const

inline

Check if the equinoctial orbit is singular, i.e., * \( i < \pi-\varepsilon_i \), or \( i > \pi+\varepsilon_i\).

Parameters

[in] tol_i Tolerance \( \varepsilon_i \) for the singularity check on the inclination.

Returns: True if the equinoctial orbit is singular, false otherwise.

◆ Omega()

Real Astro::OrbitalElements::Equinoctial::Omega ( ) const

inline

Compute the right ascension of the ascending node \( \Omega = \arctan\left(k, h\right) \) (rad).

Returns: The right ascension of the ascending node \( \Omega \).

◆ omega()

Real Astro::OrbitalElements::Equinoctial::omega ( ) const

inline

Compute the argument of periapsis \( \omega = \arctan\left(gh - fk, fh + gk\right) \) (rad).

Returns: The argument of periapsis \( \omega \).

◆ operator=() [1/2]

Equinoctial & Astro::OrbitalElements::Equinoctial::operator= ( const Equinoctial & )

default

Enable the default equinoctial orbit parameters assignment operator.

◆ operator=() [2/2]

Equinoctial & Astro::OrbitalElements::Equinoctial::operator= ( Equinoctial && )

default

Enable the default equinoctial orbit parameters move assignment operator.

◆ reset()

void Astro::OrbitalElements::Equinoctial::reset ( )

inline

Reset the equinoctial orbit parameters to NaN.

◆ sanity_check()

bool Astro::OrbitalElements::Equinoctial::sanity_check ( ) const

inline

Check if the equinoctial orbit parameters are valid, i.e., finite, and with \( p > 0 \).

Returns: True if the equinoctial orbit parameters are valid, false otherwise.

◆ u()

Real Astro::OrbitalElements::Equinoctial::u ( Real L ) const

inline

Compute the argument of latitude \( u = \omega + \Omega = \arctan\left(h\sin(L) - k\cos(L), h\cos(L) + k\sin(L)\right) \).

Parameters

[in] L The true longitude \( L \).

Returns: The argument of latitude \( u \).

◆ vector()

Vector5 Astro::OrbitalElements::Equinoctial::vector ( ) const

inline

Get the equinoctial orbit parameters as a vector.

Returns: The vector of equinoctial orbit parameters \( [p, f, g, h, k]^\top \).

Member Data Documentation

◆ f

Real Astro::OrbitalElements::Equinoctial::f {QUIET_NAN}

\( X \)-axis component of the eccentricity vector in the orbital frame (-).

◆ g

Real Astro::OrbitalElements::Equinoctial::g {QUIET_NAN}

\( Y \)-axis component of the eccentricity vector in the orbital frame (-).

◆ h

Real Astro::OrbitalElements::Equinoctial::h {QUIET_NAN}

\( X \)-axis component of the node vector in the orbital frame (-).

◆ k

Real Astro::OrbitalElements::Equinoctial::k {QUIET_NAN}

\( Y \)-axis component of the node vector in the orbital frame (-).

◆ p

Real Astro::OrbitalElements::Equinoctial::p {QUIET_NAN}

Semi-latus rectum \( p \) (UA).

The documentation for this struct was generated from the following file:

include/Astro/OrbitalElements.hh

Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Equinoctial() [1/5]

◆ Equinoctial() [2/5]

◆ Equinoctial() [3/5]

◆ Equinoctial() [4/5]

◆ Equinoctial() [5/5]

Member Function Documentation

◆ a()

◆ e()

◆ i()

◆ info() [1/2]

◆ info() [2/2]

◆ is_nonsingular()

◆ is_singular()

◆ Omega()

◆ omega()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ reset()

◆ sanity_check()

◆ u()

◆ vector()

Member Data Documentation

◆ f

◆ g

◆ h

◆ k

◆ p