Rigid-Body Kinetics

Resources:

• Chapter 3, (Fossen, 2021)

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The goal of Chapter 3 is to show that

$$M_{RB}\dot{\nu }+C_{RB}(\nu )\nu ={\tau }_{RB}$$

Where

• $M_{RB}$ is the rigid-body mass matrix
• $C_{RB}(\nu )$ is the rigid-body Coriolis and centripetal matrix due to the rotations of the body-fixed frame $\{b\}$ about the approximative inertial frame $\{n\}$,
• $\nu =[u,v,w,p,q,r{]}^T$ is the generalized velocity vector expressed in $\{b\}$
• ${\tau }_{RB}=[X,Y,Z,K,M,N{]}^T$ is a generalized vector of external forces and moments expressed in $\{b\}$.