Question about the notation and usage of direction cosine matrix in gravityEffector.cpp

[Timmi-Zhu]

Hi, I'm having some trouble understanding the notation and sign conventions in the file gravityEffector.cpp.

In the following function:

Eigen::Vector3d GravBodyData::computeGravityInertial(Eigen::Vector3d r_I, uint64_t simTimeNanos)
{
    double dt = diffNanoToSec(simTimeNanos, this->timeWritten);
    Eigen::Matrix3d dcm_PfixN = c2DArray2EigenMatrix3d(this->localPlanet.J20002Pfix).transpose();
    if (dcm_PfixN.isZero()) {
        dcm_PfixN = Eigen::Matrix3d::Identity();
    }

    Eigen::Matrix3d dcm_PfixN_dot =
        c2DArray2EigenMatrix3d(this->localPlanet.J20002Pfix_dot).transpose();
    dcm_PfixN += dcm_PfixN_dot * dt;

    // store the current planet orientation and rates
    *this->J20002Pfix = dcm_PfixN;
    *this->J20002Pfix_dot = dcm_PfixN_dot;

    // Compute position in the body-fixed reference frame and compute the gravity
    Eigen::Matrix3d dcm_NPfix = dcm_PfixN.transpose();
    Eigen::Vector3d r_Pfix = dcm_NPfix * r_I;
    Eigen::Vector3d grav_Pfix = this->gravityModel->computeField(r_Pfix);

    return dcm_PfixN * grav_Pfix;
}

My confusion is about the handling of the DCM:

• On line 4, dcm_PfixN is defined as the transpose of J20002Pfix, meaning it's actually Pfix2J2000 (from planet-fixed frame to inertial).
• But then, on line 15, this->J20002Pfix is assigned the value of dcm_PfixN, which appears to contradict the naming, as it should be J20002Pfix (from inertial to Pfix), not Pfix2J2000.

So my question is:

• Is there a missing transpose in the assignment to this->J20002Pfix? Or is J20002Pfix actually storing the DCM from Pfix to J2000 despite the name?

Any clarification would be greatly appreciated. Thanks for the awesome work on Basilisk!