Test 1 Review Flashcards

1
Q

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

A

Newton’s second law of motion.

Yechout: Pg 163

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2
Q

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

A

Applied forces and moments.

Yechout: Pg 163

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3
Q

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

A

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

Yechout: Pg 163

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4
Q

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

A

The aircraft’s CG

Yechout: Pg 164

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5
Q

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

A

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

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6
Q

Describe the orientation of the Earth-axis system.

A

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

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7
Q

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

A

Angle of attack.

Yechout: Pg 164

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8
Q

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

A

Intertial reference frame.

Yechout: Pg 164

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9
Q

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

A

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

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10
Q

True or False

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

A

True

Yechout: Pg 165

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11
Q

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

A

The angle of attack.

Yechout: Pg 165

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12
Q

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

A

Earth Axis System

Yechout: Pg 165

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13
Q

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

A

Stability axis system

Yechout: Pg 165

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14
Q

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

A

Body axis system

Yechout: Pg 166

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15
Q

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

A

Psi
Inertial z-axis

Yechout: Pg 166

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16
Q

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

A

Theta
Body attached y-axis

Yechout: Pg 166

17
Q

The roll angle is given by the Greek letter _____.

A

Phi

Yechout: Pg 166

18
Q

True or False

Euler angles must be orthogonal.

A

False

Phillips Pg 736

19
Q

What are the standard ranges of the Euler angles?

A

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

Phillips Pg 739

20
Q

True or False

The inverse of the transformation matrix is its transpose.

A

True

Phillips Pg 741

21
Q

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.

A

False

Phillips Pg 742

22
Q

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

A

Yes.
At Theta = 90 degrees.

Phillips Pg 742

23
Q

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

A

Gimbal Lock

Phillips Pg 743

24
Q

True or False

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

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
True W.Durham, Pg 20
26
True or False | The inverse of a direction cosine is equal to its transpose.
True W.Durham, Pg 20
27
True or False For direction cosine matrix T_12 T_12 * T_12 ^T == T_12
False T_12 * T_12^T == I_3 W.Durham, Pg 21
28
True or False | For a given direction cosine matrix, the squares of the row elements sum to unity.
True W.Durham, Pg 21
29
True or False | For a given direction cosine matrix, the products of offset row entries sum to 1.
False. They sum to zero. t11*t31 + t12*t32 + t13*t33 ==0 W.Durham, Pg 21
30
What numbers correspond to Euler rotations about a particular axis?
``` 1 = x rotation 2 = y rotation 3 = z rotation ``` W.Durham, Pg 21
31
What Euler sequence is commonly used in flight dynamics?
321 W.Durham, Pg 22
32
Give the common Euler angles associated with the body to the horizontal frame.
x y z phi theta psi W.Durham, Pg 27
33
Give the common Euler angles associated with the body to wind frame.
x y z 0 alpha -betta Note the negative on the sideslip angle beta. W.Durham, Pg 27
34
What is the equation for the state transition matrix?
[sI - A]^-1 W.Durham, Pg 114
35
How do you find the characteristic equation for a state-space representation?
Take the determinant of the state transition matrix [sI - A]^-1 and set it equal to zero. W.Durham, Pg 114
36
What is the modal matrix?
A matrix whose columns are the system eigenvectors. W.Durham, Pg 116
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.
True W. Durham Pg. 21
38
Which of the following Euler rotation is invalid? a) 121 b) 313 c) 112
c). You cannot use a rotation twice in succession. W.Durham Pg. 21