Admin : /* Harmonic guidance profiles */

2018-02-28T15:16:37Z

Harmonic guidance profiles

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	=== Harmonic guidance profiles ===		=== Harmonic guidance profiles ===
	The functions representing the angular velocity of the satellite and the quaternion (or the Euler angles) expressing its orientation can be represented by an harmonic profile.		The functions representing the angular velocity of the satellite and the quaternion (or the Euler angles) expressing its orientation can be represented by an harmonic profile.
	The harmonic profile is a [[Trigonometric Polynomials and Fourier Series#Fourier Series\|Fourier decomposition]] of a periodic function:		The harmonic profile is a [[User Manual 3.3 Trigonometric Polynomials and Fourier Series#Fourier Series\|Fourier decomposition]] of a periodic function:

	<math>		<math>

Admin : /* Harmonic guidance profiles */

2018-02-28T15:16:16Z

Harmonic guidance profiles

← Version précédente		Version du 28 février 2018 à 15:16
Ligne 30 :		Ligne 30 :
	=== Harmonic guidance profiles ===		=== Harmonic guidance profiles ===
	The functions representing the angular velocity of the satellite and the quaternion (or the Euler angles) expressing its orientation can be represented by an harmonic profile.		The functions representing the angular velocity of the satellite and the quaternion (or the Euler angles) expressing its orientation can be represented by an harmonic profile.
	The harmonic profile is a [~~MAT_TPOL_Home~~#~~HFourierSeries~~ Fourier decomposition] of a periodic function:		The harmonic profile is a [[Trigonometric Polynomials and Fourier Series#Fourier Series\|Fourier decomposition]] of a periodic function:

	<math>		<math>

Admin le 26 février 2018 à 16:56

2018-02-26T16:56:08Z

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	== [[File:lightBulb.png]] Tips & Tricks ==		== [[File:lightBulb.png]] Tips & Tricks ==
	{{specialInclusion prefix=$theme_sub section="Tips"/}}		{{specialInclusion prefix=$theme_sub section="Tips"/}}

			[[Category:User_Manual_3.3_Attitude]]

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Interfaces

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	== Contents ==		== Contents ==
	=== Interfaces ===		=== Interfaces ===
	~~\|=Interface\|=Summary\|=Javadoc~~		None.

	=== Classes ===		=== Classes ===

Admin le 26 février 2018 à 16:30

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Admin le 26 février 2018 à 16:18

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== Introduction ==
=== Scope ===
A guidance profile is an attitude law providing the computation of an instantaneous attitude without any reference to the satellite orbit, nor to its attitude laws sequence. The purpose of this section is to present the guidance profiles available through the Patrius library.

=== Javadoc ===
The guidance models and classes are available in the guidance package in the Patrius library.

|=(% colspan="3" %)Library|=(% colspan="6" %)Javadoc
|(% colspan="3" %)Patrius|(% colspan="6" %)[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/package-summary.html Package fr.cnes.sirius.patrius.guidance]

=== Links ===
{{specialInclusion prefix=$theme_sub section="Links"/}}

=== Useful Documents ===
{{specialInclusion prefix=$theme_sub section="UsefulDocs"/}}

=== Package Overview ===
The following diagram shows the guidance package conception:

[[File:guidage.png|center]]

== Features Description ==
=== Harmonic guidance profiles ===
The functions representing the angular velocity of the satellite and the quaternion (or the Euler angles) expressing its orientation can be represented by an harmonic profile.
The harmonic profile is a [MAT_TPOL_Home#HFourierSeries Fourier decomposition] of a periodic function:

<math>\begin{math}
S_n\left(f(x)\right) = a_0(f) + \sum_{k=1}^n\left(a_k(f)\cos\left(k x {2\pi\over T}\right) + b_k(f)\sin\left(k x {2\pi\over T}\right)\right)
\end{math}</math>

The period T is generally computed knowing the nodes crossing periods.

The Fourier coefficients (n > 0) of <math>f</math> (the angular velocity / quaternions / Euler angles function) are given by :

<math>\begin{math}
a_0(f) = {1\over T}\int_{-T/2}^{T/2} \! f(t) \, \mathrm{d}t
\end{math}</math>

<math>\begin{math}
b_0(f) = 0
\end{math}</math>

<math>\begin{math}
a_n(f) = {2\over T}\int_{-T/2}^{T/2} \! f(t) \cos\left(n t {2\pi\over T}\right) \, \mathrm{d}t
\end{math}</math>

<math>\begin{math}
b_n(f) = {2\over T}\int_{-T/2}^{T/2} \! f(t) \sin\left(n t {2\pi\over T}\right) \, \mathrm{d}t
\end{math}</math>

=== Polynomial guidance profiles ===
A polynomial guidance profile is generally composed by several segments (a segment corresponds to a time interval). Each segment contains the coefficients for the computation of a polynomial law representing the quaternion (or the Euler angles), or the angular velocity of the satellite; this polynomial law is valid only inside the time interval associated to the segment.

For a quaternion, the polynomials are defined as :

<math>Qc_k(t) = \begin{pmatrix}
\displaystyle\sum_{i=0}^n a_0_k^i \left( t-t_k \over {\Delta t} \right) \\
\displaystyle\sum_{i=0}^n a_1_k^i \left( t-t_k \over {\Delta t} \right) \\
\displaystyle\sum_{i=0}^n a_2_k^i \left( t-t_k \over {\Delta t} \right) \\
\displaystyle\sum_{i=0}^n a_3_k^i \left( t-t_k \over {\Delta t} \right)
\end{pmatrix}</math>

And for the angular velocity :

<math>\Omega c_k(t) = \begin{pmatrix}
\displaystyle\sum_{i=0}^n a_x_k^i \left( \frac{t-t_k}{\Delta t} \right) \\
\displaystyle\sum_{i=0}^n a_y_k^i \left( \frac{t-t_k}{\Delta t} \right) \\
\displaystyle\sum_{i=0}^n a_z_k^i \left( \frac{t-t_k}{\Delta t} \right)
\end{pmatrix}</math>

=== Build an harmonic guidance profile from an attitude law ===
Given :
* an [{{JavaDoc3.3}}/AttitudeLawLeg org/orekit/attitudes/AttitudeLawLeg.html],
* a [{{JavaDoc3.3}}/PVCoordinatesProvider org/orekit/utils/PVCoordinatesProvider.html],
* a [{{JavaDoc3.3}}/Frame org/orekit/frames/Frame.html],
* a [{{JavaDoc3.3}}/reference date org/orekit/time/AbsoluteDate.html] <code>tref</code>,
* a spin function period,
* a spin decomposition order,
* an [{{JavaDoc3.3}}/integration type org/orekit/attitudes/kinematics/KinematicsToolkit.IntegrationType.html],
* an integration step,

one can build an angular velocities guidance profile using the code snippet below :

<syntaxhighlight lang="java">
profile = GuidanceProfileBuilder.computeAngularVelocitiesHarmonicProfile(attitude, prop, gcrf, tref,
period, order, IntegrationType.WILCOX_4, KinematicsToolkit.DEFAULT_8HZ);
</syntaxhighlight>

== Getting Started ==
TBD

== Contents ==
=== Interfaces ===
|=Interface|=Summary|=Javadoc

=== Classes ===
|=(% colspan="3" %)Class|=(% colspan="6" %)Summary|=(% colspan="1" %)Javadoc
|(% colspan="3" %)'''KinematicsToolkit'''|(% colspan="6" %)This class contains static methods performing kinematics operations.|[{{JavaDoc3.3}}/org/orekit/attitudes/kinematics/KinematicsToolkit.html ...]
|(% colspan="3" %)'''GuidanceProfile'''|(% colspan="6" %)Abstract class representing a guidance profile.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/GuidanceProfile.html ...]
|(% colspan="3" %)'''GuidanceProfileBuilder'''|(% colspan="6" %)This class creates guidance profiles from an attitude law.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/GuidanceProfileBuilder.html ...]
|(% colspan="3" %)'''QuaternionHarmonicProfile'''|(% colspan="6" %)Object representing a quaternion guidance profile, calculated with Fourier series.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/QuaternionHarmonicProfile.html ...]
|(% colspan="3" %)'''QuaternionPolynomialProfile'''|(% colspan="6" %)Object representing a quaternion guidance profile, calculated with polynomials.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/QuaternionPolynomialProfile.html ...]
|(% colspan="3" %)'''QuaternionPolynomialSegment'''|(% colspan="6" %)Object representing a quaternion polynomial guidance profile on a segment.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/QuaternionPolynomialSegment.html ...]
|(% colspan="3" %)'''AngularVelocitiesHarmonicProfile'''|(% colspan="6" %)Represents an angular velocities guidance profile, calculated with Fourier series.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/AngularVelocitiesHarmonicProfile.html ...]
|(% colspan="3" %)'''AngularVelocitiesPolynomialProfile'''|(% colspan="6" %)Represents an angular velocities guidance profile, calculated with polynomial functions.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/AngularVelocitiesPolynomialProfile.html ...]
|(% colspan="3" %)'''Vector3DPolynomialSegment'''|(% colspan="6" %)Object representing an angular velociy polynomial guidance profile on a segment.|[{{JavaDoc3.3}}/fr/cnes/sirius/patrius/guidance/Vector3DPolynomialSegment.html ...]

== Tutorials ==
=== Tutorial 1 ===
{{specialInclusion prefix=$theme_sub section="Tuto1"/}}

=== Tutorial 2 ===
{{specialInclusion prefix=$theme_sub section="Tuto2"/}}

== [[File:lightBulb.png]] Tips & Tricks ==
{{specialInclusion prefix=$theme_sub section="Tips"/}}

User Manual 3.3 Guidance commands - Historique des versions

Admin : /* Harmonic guidance profiles */

Admin : /* Harmonic guidance profiles */

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Admin : /* Harmonic guidance profiles */

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