2.5. Thrust Guidance

This page deals with the inclusion of a thrust force into the dynamical model. Note that when using thrust, it may often be desirable to include the mass in the state vector. A good example of incorporating mass propagation is given in Use of Thrust: Thrust Force Along Velocity Vector. Details of combining mass and state propagation can be found on the Propagator Settings: Basics page.

In Tudat, we define the thrust force by two separate types of settings (which may or may not be linked):

  • The direction of the thrust.
  • The magnitude of the thrust.

In fact, when creating settings for a thrust force, the user needs to provide settings for these two aspects of the force model

std::shared_ptr< ThrustDirectionGuidanceSettings > thrustDirectionSettings;
std::shared_ptr< ThrustMagnitudeSettings > thrustMagnitudeSettings;

SelectedAccelerationMap accelerationSettingsMap;
accelerationSettingsMap[ "Vehicle" ][ "Vehicle" ].push_back( std::make_shared< ThrustAccelerationSettings >( thrustDirectionSettings, thrustMagnitudeSettings ) );

In the above code snippet, two things may stand out. First of all, we define the thrust force as one that the vehicle exerts on itself. Secondly, to define the thrust force, the user must provide two objects: one of type (derived from) ThrustDirectionGuidanceSettings and ThrustMagnitudeSettings. The settings are used to create a ThrustAcceleration acceleration object.

class ThrustAcceleration

Class contaning the properties of the thrust acceleration. Set by the settings classes described below.

2.5.1. Thrust direction

For the direction of the thrust, there are presently four available types of guidance. As is done for the acceleration models, some of the types of thrust direction require a specific derived class of ThrustDirectionGuidanceSettings, while others are defined purely by their type.

class ThrustDirectionGuidanceSettings

Base class for the setting for the direction of the thrust, in most cases not created directly by user. Important exception: thrust direction from existing orientation (see below).


The thrust-direction in the inertial frame is defined by this class. The direction of the thrust in the body-fixed frame (which may be required for the computation of the thrust) is defined in the ThrustMagnitudeSettings class.

class ThrustDirectionFromStateGuidanceSettings

In various simplified cases, the thrust direction can be assumed to be in line with either the position or velocity w.r.t. some body. As an example:

        centralBodyName, isThurstInVelocityDirection, directionIsOppositeToVector );
  • centralBodyName

    std::string which defines the name of the central body. Note that this need not be the same body as the center of propagation. For instance, the propagation of a vehicle may be done w.r.t. the Sun, while the thrust direction is computed from the state w.r.t. the Earth.

  • isThurstInVelocityDirection

    bool defining whether the thrust is colinear with velocity (if true) or position (if false) w.r.t. the central body.

  • directionIsOppositeToVector

    bool defining whether the thrust force is in the same direction, or opposite to the direction, of the position/velocity w.r.t. the central body.

class CustomThrustDirectionSettings

For a generalized thrust direction guidance, the thrust can be defined as an arbitrary function of time. This allows a broad range of options to be defined, at the expense of increased complexity (somehow this thrust direction needs to be manually defined):

        thrustDirectionFunction );
  • thrustDirectionFunction

    A std::function< Eigen::Vector3d( const double ) > returning a the thrust direction in the inertial frame as an Eigen::Vector3d (which should be of unit norm!) as a function of a double (representing time). Details on how to create such an std::function are given on Dynamic Memory: Usage Examples.


When using the CustomThrustDirectionSettings, the inertial to body-fixed rotation cannot be unambiguously defined. If you require this rotation (for instance when you also incorporate aerodynamic forces), use the CustomThrustOrientationSettings class instead.

As a possible example of how to use this function:

Eigen::Vector3d myThrustFunction( const double time, const NamedBodyMap& bodyMap )
   Eigen::Vector3d thrustDirection =
      //... define algorithm to compute thurst based on current environment

   return thrustDirection;

int main( )
   // Define environment and other settings
   NamedBodyMap bodyMap = ...

   // ...
   // ...
   // ...

   // Create custom thrust direction settings
   std::make_shared< CustomThrustDirectionSettings >(
      std::bind( &myThrustFunction, std::placeholders::_1, bodyMap );
class CustomThrustOrientationSettings

As an alternative expression for generalized thrust direction guidance, the thrust orientation can be defined as an arbitrary function of time. As with the custom thrust direction. this allows a broad range of options to be defined, at the expense of increased complexity).

        thrustOrientationFunction );
  • thrustOrientationFunction

    A std::function< Eigen::Quaterniond( const double ) > returning the rotation from body-fixed to inertial state, represented as an Eigen::Quaterniond (which should be of unit norm!) as a function of a double (representing time). See CustomThrustDirectionSettings for an example on how to realize this construction.

class MeeCostateBasedThrustDirectionSettings

By using these settings for the thrust direction, the so-called co-states of the Modified Equinoctial elements are used to determine the direction of the thrust. Details of this model are given by Kluever (2010), Boudestijn (2014) and Hogervorst (2017).

Thrust direction from existing orientation
In some cases, the vehicle’s orientation may be predetermined, either due to aerodynamic guidance of concurrent propagation of the rotational equations of motion. In such a case, the thrust direction is computed from the body-fixed thrust direction (defined in ThrustMagnitudeSettings) and the existing vehicle orientation. This thrust direction does not require a specific derived class, but instead only requires the input of thrust_direction_from_existing_body_orientation to the ThrustDirectionGuidanceSettings constructor, so:
        thrust_direction_from_existing_body_orientation, "" );

2.5.2. Thrust magnitude

To define the thrust magnitude, there are presently three available types of settings, each with its own dedicated derived class of ThrustMagnitudeSettings. We note that presently, the definition of the thrust direction in the body-fixed frame is also defined through these derived classes. In essence, the ThrustMagnitudeSettings defines all local (to the vehicle systems) settings for the thrust, while ThrustDirectionGuidanceSettings defines how the full vehicle must orient itself in space for the required thrust direction to be achieved. At present, there is no direct option for thrust-vector control (i.e. modifying the thrust direction in the body-fixed frame). If your application requires such functionality, please contact the Tudat support team. The following thrust magnitude settings are available:

class ThrustMagnitudeSettings

Base class for the thrust magnitude settings.

class ConstantThrustMagnitudeSettings
This model defines a constant thrust force and specific impulse:
    thrustMagnitude, specificImpulse, bodyFixedThrustDirection ):
  • thrustMagnitude Constant thrust magnitude to use (in Newtons, as double)
  • specificImpulse Specific impulse to use for the thrust, as double. This quantity is used when applying a mass rate model in the propagation the vehicle dynamics, relating the thrust to the mass decrease of the vehicle.
  • bodyFixedThrustDirection Body-fixed thrust direction (positive x-direction by default) as an Eigen::Vector3d. Note that this should be a unit-vector, and represents the direction opposite to the nozzle direction.
class FromFunctionThrustMagnitudeSettings
This model defines a thrust force and specific impulse that can vary with time. It requires the following settings as input:
         thrustMagnitudeFunction, specificImpulseFunction,
         isEngineOnFunction, bodyFixedThrustDirection, customUpdateFunction );
  • thrustMagnitudeFunction Thrust magnitude to use (in Newtons), as a function of time as a function of time, defined by a std::function< double( const double ) >. See below for an example on how to
  • specificImpulseFunction Specific impulse to use for the thrust as a function of time, defined by a std::function< double( const double ) >. This quantity is used when applying a mass rate model in the propagation the vehicle dynamics, relating the thrust to the mass decrease of the vehicle.
  • isEngineOnFunction Boolean defining whether the thrust should be engaged at all, as a function of time (e.g. thrust is 0 N if it returns false), defined by an std::function< bool( const double ) >. By default this function always returns true.
  • bodyFixedThrustDirection Body-fixed thrust direction (positive x-direction by default) as a std::function< Eigen::Vector3d( ) >. Note that this function should be a unit-vector, and represents the direction opposite to the nozzle direction. This setting can be used to incorporate thrust-vector control (TVC) into the thrust.
  • customUpdateFunction Function that updates any relevant aspects of the environment/system models, as a std::function< void( const double ), which is called before retrieving the thrust magnitude, specific impulse, and body-fixed thrust direction. By default, no such function is used

Note that if you wish to use a constant value (as opposed to the std::function expression) for any or all of the first three arguments, you can use lambda expression. For instance, for a variable thrust magnitude, but constant specific impulse of 300 s, you can use:

         thrustMagnitudeFunction, []( const double ){ return 300; } );

Where the last two arguments (isEngineOnFunction and bodyFixedThrustDirection) are omitted and therefore are set to their default values.

Below, we give a simple example of a class that can be used to incorporate TVC into your models. It uses a toy model, in which the thrust vector is rotated along the body-fixed y-axis, with a llinear rate in time.

class TVCGuidance

TVCGuidance( const double initialAngle, const double angleRate, const double referenceTime ):
   initialAngle_( initialAngle ), angleRate_( angleRate ), referenceTime_( referenceTime ){ }

~TVCGuidance( ){ }

void updateGuidance( const double currentTime )

   // Implement your guidance model here, using your specific algorithm
   double currentThrustAngle = initialAngle_ + angleRate_ * ( currentTime - referenceTime );
   bodyFixedThrustDirection_ << std::cos( currentThrustAngle ), 0.0, std::sin( currentThrustAngle );

   // Ensure that direction is a unit vector
   bodyFixedThrustDirection_.normalize( );

Eigen::Vector3d getBodyFixedThrustDirection( )
   return bodyFixedThrustDirection_;


   Eigen::Vector3d bodyFixedThrustDirection_;

   double initialAngle_;

   double angleRate_;

   double referenceTime_;


A real guidance model will likely depend on the current environment, and will therefore often have a NamedBodyMap as an input to its constructor.

The ThrustMagnitudeSettings are then created as follows, with an initial thrust angle of -0.01 radians (at t=86400 s since J2000) and an angle rate 1.0E-6 radians per second:

// Create TVC guidance object
std::shared_ptr< TVCGuidance > tvcGuidance = std::make_shared< TVCGuidance >(
   -0.01, 1.0E-6, 86400.0 );

// Retrieve required functions from TVC object
std::function< void( const double ) > updateFunction =
   std::bind( &TVCGuidance::updateGuidance, tvcGuidance, std::placeholders::_1 );
std::function< Eigen::Vector3d( ) > thrustDirectionFunction =
   std::bind( &TVCGuidance::getBodyFixedThrustDirection );

// Create thrust magnitude settings, with constant thrust magnitude and specific impulse
double thrustMagnitude = 1.0E3;
double specificImpulse = 300;
std::shared_ptr< ThrustMagnitudeSettings > thrustMagnitudeSettings =
   std::make_shared< FromFunctionThrustMagnitudeSettings >(
      [ = ]( const double ){ return thrustMagnitude; },
      [ = ]( const double ){ return specificImpulse; },
      [ ]( const double ){ return true; },
      updateFunction );

Note that we use a constant thrust magnitude (1 kN) and specific impulse (300 s) here, and focus the example on showing how to incorporate variable body-fixed thrust direction. If so desired, the above could also be used for variable thrust mangitude/specific impulse, by modifying any guidance class(es).


You can combined thrust and aerodynamic guidance, by implementing any required thrust guidance functions into your own custom derived class of AerodynamicGuidance

class FromBodyThrustMagnitudeSettings
A Body object may be endowed with a VehicleSystems property, which defines the suite of hardware that it carries. One of the systems that may be defined in the VehicleSystems object which is a list of EngineModel objects (stored in a list). This class creates thrust magnitude settings that use the thrust from one or all of the EngineModel objects that a vehicle is endowed with. In such a situation, the thrust direction, force and specific impulse are taken from the EngineModel. It requires the following settings:
         useAllEngines, thrustOrigin );
  • useAllEngines A bool defining whether all engines (i.e. all entries in the engineModels member of the VehicleSystems object in the vehicle’s Body object) are to be used, or only a single engine.
  • thrustOrigin A std::string with the name of the engine that is to be used for the thrust (to be empty if useAllEngines is true)
class EngineModel

Class in which the model of the engine is saved. Settings similar to those in the previous two thrust magnitude settings may be stored. However, using the interface with an engine model allows a more integrated systems/trajectory simulation to be performed, with applications in e.g. MDO. It allows multiple engine models, each with their own properties, to be defined.


Currently this class in under development, note that this is still a priliminary version.