What are the Euler angles for x, y, and z?
$$\Phi, \Theta, \Psi$$
What is the x rotation matrix for a counterclockwise rotation?
$$\begin{bmatrix} 1 & 0 & 0 \\ 0 & cos(\theta) & sin(\theta) \\ 0 & -sin(\theta) & cos(\theta) \\ \end{bmatrix}$$
What is the y rotation matrix for a counterclockwise rotation?
$$\begin{bmatrix} cos(\theta) & 0 & -sin(\theta) \\ 0 & 1 & 0 \\ sin(\theta) & 0 & cos(\theta) \\ \end{bmatrix}$$
What is the z rotation matrix for a counterclockwise rotation?
$$\begin{bmatrix} cos(\theta) & sin(\theta) & 0 \\ -sin(\theta) & cos(\theta) & 0 \\ 0 & 0 & 1 \\ \end{bmatrix}$$
How do you convert from inertial to NED?
$$\begin{bmatrix} v_x \\ v_y \\ v_z \\ \end{bmatrix} = \begin{bmatrix} vcos(\gamma)cos(\psi) \\ vcos(\gamma)sin(\psi) \\ -vsin(\gamma) \\ \end{bmatrix}$$
How do you convert from inertial to NWU?
$$\begin{bmatrix} v_x \\ v_y \\ v_z \\ \end{bmatrix} = \begin{bmatrix} vcos(\gamma)cos(\psi) \\ -vcos(\gamma)sin(\psi) \\ vsin(\gamma) \\ \end{bmatrix}$$
How do you convert from inertial to NED using inclination?
$$\begin{bmatrix} v_x \\ v_y \\ v_z \\ \end{bmatrix} = \begin{bmatrix} vcos(\gamma)sin(\psi) \\ vcos(\gamma)cos(\psi) \\ -vsin(\gamma) \\ \end{bmatrix}$$
What values go into the DCM for an ECI to NED relation?
$$\phi = 0, \theta = -(90+\lambda), \psi = \delta$$
What dimension is a quaternion variable?
4-D
What are the components to a quaternion variable?
3 are positional and one is rotational.
In the wind axes frame, how do you calculate alpha, given the velocity vector?
$$\alpha=\tan^{-1}(\frac{v_z}{v_x})$$
In the wind axes frame, how do you calculate beta, given the velocity vector?
$$\beta=\tan^{-1}(\frac{v_y}{\sqrt{v_x^2+v_z^2}})$$
In static stability, what corresponds to Statically Stable, Statically Neutrally Stable, and Statically Unstable?
Positive stability (tends to return to trim), neutral stability (stays at disturbed position), and negative stability (tendency to move away from equilibrium).
In dynamic stability, what corresponds to Dynamically Stable, Dynamically Marginally Stable, and Dynamically Unstable?
Stays within constricting envelope, stays in same position or oscillates at a constant amplitude, and immediately diverges or has divergent oscillations.
What is this stability?
Stable
What is this stability?
Stable
What is this stability?
Marginally Stable
What is this stability?
Unstable
What is this stability?
Unstable
What is this stability?
Unstable
What is this stability?
Unstable
What is this stability?
Unstable
What type of stability occurs when the cg is ahead of the neutral point, at the neutral point, and aft the neutral point?
Statically stable, statically neutrally stable, and statically unstable.
What happens when the fuselage is added to the wing analysis?
The AC shifts forward, the lift curve slope increases, and a negative moment is added about the AC.
For longitudinal static stability, how many modes are there and what are they called?
2 modes. Phugoid and short period mode.
In lateral static stability, how many modes are there and what are they called?
3 modes. Roll, dutch mode, and spiral mode where spiral mode has 2 sub-modes: directional divergence and spiral divergence.
What order is the Dutch Roll mode (how many eigenvalues will it have)?
2nd order with 2 eigenvalues which are a complex conjugate pair.
What order is the Roll mode (how many eigenvalues will it have)?
1st order, so only 1 real eigenvalue.
What order is the Spiral mode (how many eigenvalues will it have)?
1st order, so only 1 real eigenvalue.
How does a swept wing contribute to lateral stability?
Positive.
How does a bottom-mounted wing with a dihedral effect contribute to static lateral stability?
Positive.
Top-mounted wings contribute a positive static lateral stability, but it is often too large for practical turning. How can this be reduced?
An anhedral effect to the top-mounted wing.
What contribution does a straight bottom-mounted wing have on static lateral stability?
Negative.
How do flaps and spoilers affect lateral stability?
They destabilize.