Chapter 3.3 Rigid-body equations of motion

$$\begin{array}{c}{f}_b^b={\left[\begin{array}{ccc}X& Y& Z\end{array}\right]}^T\text{— force trough the CO expressed in body frame}\\ m_b^b={\left[\begin{array}{ccc}K& M& N\end{array}\right]}^T\text{— moment about the CO expressed in body frame}\\ v_b^b={\left[\begin{array}{ccc}u& v& w\end{array}\right]}^T\text{— linear velocity of the CO relative to origin of NED frame expressed in body frame}\\ {\omega }_b^b={\left[\begin{array}{ccc}p& q& r\end{array}\right]}^T\text{— angular velocity of body frame relative to NED frame expressed in body frame}\\ r_b^b={\left[\begin{array}{ccc}{x}_g& y_g& z_g\end{array}\right]}^T\text{— vector from the CO to the CG expressed in body frame}\end{array}$$

Rigid-body system inertia matrix

rbody.m

Coriolis- centripetal matrix from system inertia matrix

Lagrangian parameterization

m2c.m

Linear velocity- independent parameterization

Can also be computed for nonzero values of:

$$r_{bg}^b$$