Chapter 3 - Rigid-Body Kinetics

Resources:

• Ch. 3 Fossen
• L1b

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The overall goal of the chapter 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 rotation 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 $\{b\}$ and ${\tau }_{RB}=[X,Y,Z,K,M,N{]}^T$ is a generalized vector of external forces and moments expressed in $\{b\}$.