![[Fig1-eps-converted-to.pdf]] Figure [[Fig1-eps-converted-to.pdf|1]] is of a general variable mass system (GVMS). It comprises a consumable rigid base $B$ and a fluid phase $F$. A massless shell $C$ of constant volume $V_0$ and constant surface area $S_0$ is rigidly attached to $B$. It is assumed that mass can enter or exit $C$ through the region represented as a dashed circle of radius $R$. At every instant, the shell and everything within it is considered to be the system of interest. ## Kinematics First, note from the figure that: $ \mathbf{r} = \mathbf{r^*} + \mathbf{p} $ Inertial velocity of $P$ $ {^N\mathbf{v}^P}= {^N\mathbf{v}^O} + (^N\boldsymbol{\omega}^B \times \mathbf{r}) + {^B\mathbf{v}^P} $ and inertial velocity of $S^*$ $ {^N\mathbf{v}^*}= {^N\mathbf{v}^O} + (^N\boldsymbol{\omega}^B \times \mathbf{r^*}) + {^B\mathbf{v}^*} $ So, we can rewrite the inertial velocity of $P$ relative to $S^*$ as $ {^N\mathbf{v}^P}= {^N\mathbf{v}^*} + (^N\boldsymbol{\omega}^B \times \mathbf{p}) + ( {^B\mathbf{v}^P} - {^B\mathbf{v}^*}) $ ## Next notes [[2a1 Lagrangian of GVMS]] [[2a2 VMS Equations of Attitude Motion about mass centre]]