ggdisturbance#

namespace saltro
namespace disturbances
class GGDisturbance : public Disturbance#
#include <ggdisturbance.h>

Gravity gradient (GG) disturbance model.

Computes torque due to the differential gravitational force (gravity gradient) acting on a spatially extended spacecraft. The torque arises because the spacecraft’s geometry extends over a distance comparable to the gravitational field gradient.

The gravity gradient torque is approximated as:

\[ \boldsymbol{\tau}_{\text{gg}} = 3 \frac{\mu}{r^5} \mathbf{r} \times (\mathbf{J}\,\mathbf{r}) \]

where:

  • \(\mu\) is Earth’s gravitational parameter

  • \(\mathbf{r}\) is the spacecraft position (body-fixed frame)

  • \(\mathbf{J}\) is the spacecraft’s moment of inertia tensor

This effect is typically small but important for high-precision attitude control and for large spacecraft with substantial moment of inertia asymmetry.

Public Types

using Vec3 = Eigen::Vector3d#
using Mat33 = Eigen::Matrix3d#
using BaseState = ::Disturbance::BaseState#
using Mat34 = ::Disturbance::Mat34#
using Mat44 = ::Disturbance::Mat44#
using T443 = ::Disturbance::T443#

Public Functions

GGDisturbance() = default#

Default constructor; initializes with identity inertia.

explicit GGDisturbance(const Mat33 &inertia)#

Construct a gravity gradient disturbance with specified inertia.

Parameters:

inertia – 3×3 moment of inertia tensor (kg·m²).

inline void setInertia(const Mat33 &inertia)#

Set the spacecraft’s moment of inertia tensor.

Parameters:

inertia – 3×3 inertia matrix.

inline const Mat33 &inertia() const#

Get the spacecraft’s moment of inertia tensor.

Returns:

Const reference to the 3×3 inertia matrix.

virtual Vec3 torque(const BaseState &x, const DisturbanceConfig &dist_cfg) const override#

Compute gravity gradient torque.

The position vector must be in the body-fixed reference frame for correct computation of the cross product with the inertia tensor.

Parameters:

  • x – Base state (quaternion for frame transformations).

  • dist_cfg – Disturbance configuration (unused for GG).

Returns:

3D gravity gradient torque.

Vec3 torque(const BaseState &x, const DisturbanceConfig &dist_cfg, const Vec3 &r_body, const Mat33 &J) const#

Compute gravity gradient torque with explicit position.

Extended interface allowing direct position input in body frame.

Parameters:

  • x – Base state.

  • dist_cfg – Disturbance configuration.

  • r_body – Position vector in body frame (m).

  • J – Inertia tensor (kg·m²).

Returns:

3D gravity gradient torque.

Mat34 dtorque_dq(const BaseState &x, const DisturbanceConfig &dist_cfg, const Vec3 &r_body, const Mat33 &J, const Mat34 &dr_dq) const#

Jacobian of gravity gradient torque with respect to quaternion.

Parameters:

  • x – Base state.

  • dist_cfg – Disturbance configuration.

  • r_body – Position in body frame.

  • J – Inertia tensor.

  • dr_dq – Jacobian of position with respect to quaternion (4×3).

Returns:

3×4 Jacobian matrix.

T443 ddtorque_dqdq(const BaseState &x, const DisturbanceConfig &dist_cfg, const Vec3 &r_body, const Mat33 &J, const Mat34 &dr_dq, const std::array<Mat44, 3> &d2r_dq2) const#

Hessian of gravity gradient torque with respect to quaternion.

Parameters:

  • x – Base state.

  • dist_cfg – Disturbance configuration.

  • r_body – Position in body frame.

  • J – Inertia tensor.

  • dr_dq – Jacobian of position with respect to quaternion.

  • d2r_dq2 – Array of three 4×4 Hessian matrices for position.

Returns:

Tensor3 with 3 slices of 4×4 matrices.

Private Members

Mat33 inertia_ = Mat33::Identity()#

Moment of inertia tensor.