Processed vs. Propagated State Elements

In Tudat, we distinguish between ‘processed’ and ‘propagated’ state elements, wi. Below, we describe distinction. Note that in most cases, users will have to specify (for initial states) or interact with (for custom models) the processed states.

Processed Elements

The processed elements are used to describe the state of the object(s) in any place other than the state vector that is being solved for by the numerical integrator.

For the supported dynamics types, the following formulations are defined to be the processed formulation:

  • Translational Motion: Cartesian coordinates (w.r.t central body, if relevant)

  • Rotational Motion: Quaternions defining rotation from inertial to body-fixed frame (see Definition of rotational state), angular velocity vector of the body in body-fixed frame

  • Mass Dynamics: Current mass (no other formulation is used)

You will find and need to use processed coordinates in these scenarios:

Internally, Tudat uses the processed state in the following places:

  • To update the environment model of an object (this also means that the states extracted from the body are expressed In the processed coordinates);

  • To update the acceleration model of an object.

Propagated Elements

The propagated coordinates, on the other hand, are used only to describe the state in the actual differential equations being used. A list of options for translational and rotational dynamics is given in TranslationalPropagatorType and RotationalPropagatorType, respectively. The choice of formulation for translational and rotational motion is specified when calling the translational() and rotational() functions, respectively.

In Tudat, you will find the propagated elements in the following place:

Internally, Tudat uses the propagated state in the following place:

As a user, you will generally only interact with the processed coordinates, but you will have the choice over which propagated coordinate to use for propagation/integration. Even though you may rarely interact with the propagated coordinates, a judicious choice of formulation of equations of motion (e.g., definition of propagated coordinates) can have a significant influence on the quality of your numerical results.


Since the processed coordinates are used to update the environment and accelerations of the bodies, but the propagated coordinates are the ones used in propagation, you can see that whenever the processed and propagated coordinates differ, there is a need to convert between the two at every time step (or even multiple times, if the time step is divided in multiple steps for integration). Therefore, this leads to a set of extra operations to be perfomed during propagation, which may in turn lead to a longer computation time for a single evaluatuon of the state derivative and/or increased numerical error. However, these aspects are rarely influential.


Another fact to consider, is that sometimes there may be a difference between the size of the processed and propagates states. For instance, a Cartesian state is expressed with 6 elements, but the USM7 state with 7. This may lead to some confusion when extracting the results, so keep this in mind.