Test 1 Review

Question 1

The equations of motion for an aircraft in flight are found by applying ______.

Answer 1

Newton’s second law of motion.

Yechout: Pg 163

Question 2

What does the right-hand side of the EOM provide?

Answer 2

Applied forces and moments.

Yechout: Pg 163

Question 3

What does the left-hand side of the EOM provide?

Answer 3

The aircraft response (the accelerations multiplied by the mass).

Yechout: Pg 163

Question 4

For the body axis system, where is the origin (usually) placed?

Answer 4

The aircraft’s CG

Yechout: Pg 164

Question 5

Describe the axis orientation of the body system with respect to the aircraft geometry.

Answer 5

The x-axis points from the CG out the nose of the aircraft. The z-axis lies in the longitudinal plane of symmetry and points down away from the belly. The y- axis points outward from the right wing completing the right-hand triad.

Yechout: Pg 164

Question 6

Describe the orientation of the Earth-axis system.

Answer 6

The axis is fixed to the earth’s surface with the z-axis pointing toward the Earth’s core, the x-axis points north and the y-axis is east.

Yechout: Pg 164

Question 7

The stability axis system is rotated relative to the body axis system through the __________.

Answer 7

Angle of attack.

Yechout: Pg 164

Question 8

Newton’s second law is only valid in an _____.

Answer 8

Intertial reference frame.

Yechout: Pg 164

Question 9

For the stability axis system, describe the orientation of the x-axis.

Answer 9

The x-axis points in the direction of the projection of the relative wind onto the xz plane of the aircraft.

Yechout: Pg 164-165

Question 10

True or False

In the stability axis system, the y-axis is coincident with the y-axis in the body system.

Answer 10

True

Yechout: Pg 165

Question 11

In the stability axis system, the z-axis is tiled toward the tail through _______.

Answer 11

The angle of attack.

Yechout: Pg 165

Question 12

The gravitational force on the aircraft is usually expressed in what coordinate system?

Answer 12

Earth Axis System

Yechout: Pg 165

Question 13

The aerodynamic forces on the aircraft are usually expressed in what coordinate system?

Answer 13

Stability axis system

Yechout: Pg 165

Question 14

The thrust forces on the aircraft are usually expressed in what coordinate system?

Answer 14

Body axis system

Yechout: Pg 166

Question 15

The azimuth angle is given by the Greek letter ____. This angle describes a rotation about the _____ axis.

Answer 15

Psi
Inertial z-axis

Yechout: Pg 166

Question 16

The elevation angle is given by the Greek letter _____. The elevation angle is a rotation of the aircraft about the _____ axis.

Answer 16

Theta
Body attached y-axis

Yechout: Pg 166

Question 17

The roll angle is given by the Greek letter _____.

Answer 17

Phi

Yechout: Pg 166

Question 18

True or False

Euler angles must be orthogonal.

Answer 18

False

Phillips Pg 736

Question 19

What are the standard ranges of the Euler angles?

Answer 19

-180 < Phi < 180
-90 < Theta <90
0<= Psi <=360

Phillips Pg 739

Question 20

True or False

The inverse of the transformation matrix is its transpose.

Answer 20

True

Phillips Pg 741

Question 21

True or False
With respect to the aircraft kinematic equations; the inverse of the matrix relating the roll rates to the time derivatives of the Euler angles will equal its transpose.

Answer 21

False

Phillips Pg 742

Question 22

With respect to the Euler angles, is there a mathematical singularity, and if so, describe it.

Answer 22

Yes.
At Theta = 90 degrees.

Phillips Pg 742

Question 23

The singularity present in the integration of the Euler angles is commonly called ____.

Answer 23

Gimbal Lock

Phillips Pg 743

Question 24

True or False

The weight force expressed in the body axis system is independent of the aircraft’s heading.

Answer 24

True

Question 25

True or False
For a direction cosine matrix, if a column is given by x1 x2, and x3, the following equation holds for any column.
x1^2 + x2^2 + x3^2 = 1

Answer 25

True

W.Durham, Pg 20

Question 26

True or False

The inverse of a direction cosine is equal to its transpose.

Answer 26

True

W.Durham, Pg 20

Question 27

True or False
For direction cosine matrix T_12
T_12 * T_12 ^T == T_12

Answer 27

False
T_12 * T_12^T == I_3

W.Durham, Pg 21

Question 28

True or False

For a given direction cosine matrix, the squares of the row elements sum to unity.

Answer 28

True

W.Durham, Pg 21

Question 29

True or False

For a given direction cosine matrix, the products of offset row entries sum to 1.

Answer 29

False. They sum to zero.

t11t31 + t12t32 + t13*t33 ==0

W.Durham, Pg 21

Question 30

What numbers correspond to Euler rotations about a particular axis?

Answer 30

1 = x rotation
2 = y rotation
3 = z rotation 

W.Durham, Pg 21

Question 31

What Euler sequence is commonly used in flight dynamics?

Answer 31

321

W.Durham, Pg 22

Question 32

Give the common Euler angles associated with the body to the horizontal frame.

Answer 32

x y z
phi theta psi

W.Durham, Pg 27

Question 33

Give the common Euler angles associated with the body to wind frame.

Answer 33

x y z
0 alpha -betta

Note the negative on the sideslip angle beta.

W.Durham, Pg 27

Question 34

What is the equation for the state transition matrix?

Answer 34

[sI - A]^-1

W.Durham, Pg 114

Question 35

How do you find the characteristic equation for a state-space representation?

Answer 35

Take the determinant of the state transition matrix [sI - A]^-1 and set it equal to zero.

W.Durham, Pg 114

Question 36

What is the modal matrix?

Answer 36

A matrix whose columns are the system eigenvectors.

W.Durham, Pg 116

Question 37

True or False
With respect to Euler angles, the order of selection of axes in the rotation is arbitrary, but the same axis may not be used twice in succession.

Answer 37

True

W. Durham Pg. 21

Question 38

Which of the following Euler rotation is invalid?

a) 121
b) 313
c) 112

Answer 38

c). You cannot use a rotation twice in succession.

W.Durham Pg. 21