# Simplified rocket lateral dynamics model sign convention

I had came across a simplified simplified rocket lateral dynamics model seen in this image below:

. It has vanes at the exit which generate lift force and can control the rocket orientation- the lift force is actually a ''side force'' which can impose moments about the rockets centre of gravity. The link :https://github.com/build-week/hover-jet/blob/feature/start-design-scripts/design-scripts/jet_vane_speed.ipynb contains more infomation by the author. In it, linear and angular momentum equations are present for the current orientation.

Fj: engine thrust

Lv: lift force

Dv: drag force

rv: Distance from vanes to rocket centre of mass

alpha: vane angle of attack

theta: pitch over angle of the rocket

angular momentum:

$$L_v r_v = I \ddot{\theta}$$

Linear momentum:

$$-(F_j - D_v) \sin\theta + L_v \cos\theta = m \ddot{x}$$

I don't seem to understand the sign convention for the lift force generated by the vanes in these equations; at the current angle of attack seen in the image, the lift force Lv would be in a south-west direction. In the equations, it seems the author took it in the north-east direction. In other words, should the equations instead read as:

$$-L_v r_v = I \ddot{\theta}$$

$$-(F_j - D_v) \sin\theta - L_v \cos\theta = m \ddot{x}$$ Does anyone happen to know why he made the signs by Lv positive instead? Any advice is appreciated

• What is the "sign" of $r_v$ ? Maybe the author started from the expression for moment of a force : $r \times f$.
– AJN
Commented Jul 26, 2021 at 4:15
• @AJN thanks for pointing that out, I missed adding info about r_v. I believe it is the distance from the vanes to the rockets centre of mass Commented Jul 26, 2021 at 7:14
• for that matter, what is the sign of angle θ, as the diagram uses a most unconventional way of measuring the angle? Commented Jul 26, 2021 at 7:40
• @PcMan it seems the author took theta as an acute angle, and manually added the negetive/positive signs Commented Jul 26, 2021 at 12:22

Notice that with the angular momentum equation: $$L_vr_v = I\ddot{\theta}$$ We would expect a positive $$L_v$$ to increase $$\theta$$. Similarly with the linear momentum equation, a positive $$L_v$$ should increase $$x$$.
Now for the confusion: The author has drawn an $$L_v$$ vector on his/her diagram pointing in the negative direction! They show the positive direction with that dashed line. This would then be carried through the equations with a built-in negative, giving the same result as your rewritten equations.