Gravity gradient torque function modeling two-body gravity.
The spacecraft body is subject to a non-uniform gravity field which can cause external torques about the body center. This non-uniformity is due to the inverse-square relation of the force field and the distance from the mass center, as well as a non-spherical, non-homogenous central body (such as the Earth, but especially true for asteroid or irregularly shaped central bodies).
The gravity gradient torque about the body principal axes is:
![\[ {\bf T}_{gg} = 3\omega _c ^2 {\bf o_3} ^{\times} {\bf{I}}{\bf o_3} \]](form_45.png)
where 
and 
is the 
column of the body-orbital rotation.
For enhanced accuracy, a better model would include a higher order gravity field that is dependent on the spacecraft's position and the central body's orientation. Furthermore, it is useful to analyze the spacecraft's moment of inertia matrix to evaluate its stability due to the gravity gradient disturbance torque.
- Parameters:
-
_currentTime current simulation time _currentOrbitState current orbit state, including representation and reference frame _currentAttitudeState current attitude state, including rotation and reference frame _parameterList EnvFuncParamaterType parameter list for external variables = [ 
], Moments of Inertia, gravitational parameter
- Returns:
- This force functions returns a 3-element vector of torques (Tx,Ty,Tz) due to gravity gradient using a two-body simplified force model.
Definition at line 82 of file GravityFunctions.h.
References _, O_SESSAME::OrbitStateRepresentation::GetPositionVelocity(), O_SESSAME::AttitudeState::GetRotation2Orbital(), O_SESSAME::OrbitState::GetStateRepresentation(), O_SESSAME::Matrix, O_SESSAME::norm2(), O_SESSAME::skew(), and O_SESSAME::Vector.
Referenced by SetupEnvironment().
