# What does "Poisson's formula" refer to in this calculation?

I am not entirely sure if this question belongs to this forum, but I don't know where else to ask.

I am following a Rocket Propulsion course. There is a section concerned with the Velocity Equations during Atmospheric Re-Entry. Where:

• L is Lift force
• D is Drag force
• $\phi$ is the flight path angle
• $\mathbf{e_r}$, $\mathbf{e_v}$, $\mathbf{e_L}$, etc. are unit vectors in the direction of the subscripted parameters

The derivation of the equations is clear for me, I just don't know where this Poisson's formula comes from. I googled it and I just find the well known differential equation or information about the statistical distribution. I know this should be a basic concept but right now it looks like I am missing something.

Thank you very much

• Probably several people will recognize these equations instantly, but as a courtesy to us remaining readers could you perhaps mention what $\mathbf{e}$, $\mathbf{D}$, and $\mathbf{L}$ and maybe $\mathbf{\phi}$? Thanks!
– uhoh
Sep 13, 2018 at 18:37
• My apologies, I will edit now the question. Sep 13, 2018 at 18:55

show that the derivatives of the moving unit vectors are perpendicular to $\mathbf{\omega}$. The physical significance of this vector, which is called the angular velocity of the moving reference frame with respect to the fixed reference frame, is illustrated in the next section.
$$\frac{d\mathbf{i}}{dt} = \mathbf{\omega} \times\mathbf{i}$$ $$\frac{d\mathbf{j}}{dt} = \mathbf{\omega} \times\mathbf{j}$$ $$\frac{d\mathbf{k}}{dt} = \mathbf{\omega} \times\mathbf{k}$$
where $\mathbf{\omega} = p\mathbf{i} + q\mathbf{j} + r\mathbf{k}$.