Skip to content
GitLab
Menu
Projects
Groups
Snippets
Loading...
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Orekit
Orekit
Commits
59c2d116
Commit
59c2d116
authored
Dec 24, 2021
by
Luc Maisonobe
Browse files
Improved documentation.
parent
0f4300d8
Changes
1
Hide whitespace changes
Inline
Side-by-side
src/main/java/org/orekit/forces/maneuvers/jacobians/TriggerDate.java
View file @
59c2d116
...
...
@@ -25,6 +25,7 @@ import org.orekit.forces.maneuvers.Maneuver;
import
org.orekit.forces.maneuvers.trigger.ManeuverTriggersResetter
;
import
org.orekit.propagation.AdditionalStateProvider
;
import
org.orekit.propagation.SpacecraftState
;
import
org.orekit.propagation.integration.AdditionalDerivativesProvider
;
import
org.orekit.time.AbsoluteDate
;
import
org.orekit.utils.TimeSpanMap
;
...
...
@@ -41,7 +42,14 @@ import org.orekit.utils.TimeSpanMap;
* \(\frac{\partial y_t}{\partial t_1}\).
* </p>
* <p>
* After trigger time \(t_1\) (according to propagation direction),
* There are two parts in this Jacobian: the primary part corresponds to the full contribution
* of the acceleration due to the maneuver as it is delayed by a small amount \(dt_1\), whereas
* the secondary part corresponds to change of acceleration after maneuver start as the mass
* depletion is delayed and therefore the spacecraft mass is different from the mass for nominal
* start time.
* </p>
* <p>
* The primary part is computed as follows. After trigger time \(t_1\) (according to propagation direction),
* \[\frac{\partial y_t}{\partial t_1} = \pm \frac{\partial y_t}{\partial y_1} f_m(t_1, y_1)\]
* where the sign depends on \(t_1\) being a start or stop trigger and propagation being forward
* or backward.
...
...
@@ -57,7 +65,8 @@ import org.orekit.utils.TimeSpanMap;
* \[\frac{\partial y_t}{\partial y_1} = \frac{\partial y_t}{\partial y_0} \left(\frac{\partial y_1}{\partial y_0}\right)^{-1}\]
* </p>
* <p>
* The Jacobian column can therefore be computed using the following closed-form expression:
* The contribution of the primary part to the Jacobian column can therefore be computed using the following
* closed-form expression:
* \[\frac{\partial y_t}{\partial t_1}
* = \pm \frac{\partial y_t}{\partial y_0} \left(\frac{\partial y_1}{\partial y_0}\right)^{-1} f_m(t_1, y_1)
* = \frac{\partial y_t}{\partial y_0} c_1\]
...
...
@@ -65,8 +74,8 @@ import org.orekit.utils.TimeSpanMap;
* by solving \(\frac{\partial y_1}{\partial y_0} c_1 = \pm f_m(t_1, y_1)\).
* </p>
* <p>
* As the column is generated using a closed-form expression, this generator
implements
* the {@link AdditionalStateProvider} interface and stores the column directly
* As the
primary part of the
column is generated using a closed-form expression, this generator
*
implements
the {@link AdditionalStateProvider} interface and stores the column directly
* in the primary state during propagation.
* </p>
* <p>
...
...
@@ -74,6 +83,28 @@ import org.orekit.utils.TimeSpanMap;
* if propagation starts outside of the maneuver and passes over \(t_1\) during integration.
* </p>
* <p>
* The secondary part is computed as follows. We have acceleration \(\vec{\Gamma} = \frac{\vec{F}}{m}\) and
* \(m = m_0 - q (t - t_s)\), where \(m\) is current mass, \(m_0\) is initial mass and \(t_s\) is
* maneuver trigger time. A delay \(dt_s\) on trigger time induces delaying mass depletion.
* We get:
* \[d\vec{\Gamma} = \frac{-\vec{F}}{m^2}} dm = \frac{-\vec{F}}{m^2} q dt_s = -\vec{Gamma}\frac{q}{m} dt_s\]
* From this total differential, we extract the partial derivative of the acceleration
* \[\frac{\partial\vec{\Gamma}}{\partial t_s} = -\vec{Gamma}\frac{q}{m}\]
* </p>
* <p>
* The contribution of the secondary part to the Jacobian column can therefore be computed by integrating
* the partial derivative of the acceleration, to get the partial derivative of the position.
* </p>
* <p>
* As the secondary part of the column is generated using a differential equation, a separate
* underlying generator implementing the {@link AdditionalDerivativesProvider} interface is set up to
* perform the integration during propagation.
* </p>
* <p>
* This generator takes care to sum up the primary and secondary parts so the full column of the Jacobian
* is computed.
* </p>
* <p>
* The implementation takes care to <em>not</em> resetting \(c_1\) at propagation start.
* This allows to get proper Jacobian if we interrupt propagation in the middle of a maneuver
* and restart propagation where it left.
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment