An asymmetric top (I1 < 12 < I3) executes torque-free motion with 2E12 = L². If the angular velocity w initially lies in the plane of ê1 and ê3, integrate Euler's equations to obtain the solution I w₁(t) = Woo 12 (13 - 12) 11 (13-11)] 1/2 sech(t/T), w2 (t) =&oo tanh(t/T), w3 (t): sech(t/T), where wo = 2E/L and 7= w[(13-12) (12 - 11)/(1311)]-1/2. Discuss the time dependence of w²= ||² and sketch the motion of as seen in the body-fixed frame. 12 (12-11) 1¹/2 13(13-11). = Woo
An asymmetric top (I1 < 12 < I3) executes torque-free motion with 2E12 = L². If the angular velocity w initially lies in the plane of ê1 and ê3, integrate Euler's equations to obtain the solution I w₁(t) = Woo 12 (13 - 12) 11 (13-11)] 1/2 sech(t/T), w2 (t) =&oo tanh(t/T), w3 (t): sech(t/T), where wo = 2E/L and 7= w[(13-12) (12 - 11)/(1311)]-1/2. Discuss the time dependence of w²= ||² and sketch the motion of as seen in the body-fixed frame. 12 (12-11) 1¹/2 13(13-11). = Woo
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Question 1
![1. An asymmetric top (11 < I2 I3) executes torque-free motion with 2EI2 = L2. If the angular velocity w initially
lies in the plane of ê1 and ê3, integrate Euler's equations to obtain the solution
I
2
w₁(t) = woo
3
12 (13
I1(13-11).
}
20
8
J
where woo = 2E/L and T = w[(13 - 12) (I2 − I1)/(1311)]-1/2. Discuss the time dependence of w²= ||² and sketch
the motion of as seen in the body-fixed frame.
2. A Thumbtack on an inclined plane
30
F4
1/2
sech (t/T), w₂ (t) =
0
▬
%
Q Search
S
ㅏ
LD
6
F6
=coo tanh(t/T),
>
P
7
C
G
C
A rigid body in the shape of a thumbtack formed from a
thin disk of mass M and radius a and a massless stem is
placed on an inclined plane that makes an anale a with
O D
8
00
w3 (t)
FB
= Wx
H
9
[12(12-11)
13(13-11).
12 (121) sech(1/7).
F9
1/2
0
F10
P
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b65ef36-cf51-4f81-80a6-74e205c9e9b1%2F9942440d-1ebb-4e8d-b367-f320b6aaf4ae%2Fnhnx02f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. An asymmetric top (11 < I2 I3) executes torque-free motion with 2EI2 = L2. If the angular velocity w initially
lies in the plane of ê1 and ê3, integrate Euler's equations to obtain the solution
I
2
w₁(t) = woo
3
12 (13
I1(13-11).
}
20
8
J
where woo = 2E/L and T = w[(13 - 12) (I2 − I1)/(1311)]-1/2. Discuss the time dependence of w²= ||² and sketch
the motion of as seen in the body-fixed frame.
2. A Thumbtack on an inclined plane
30
F4
1/2
sech (t/T), w₂ (t) =
0
▬
%
Q Search
S
ㅏ
LD
6
F6
=coo tanh(t/T),
>
P
7
C
G
C
A rigid body in the shape of a thumbtack formed from a
thin disk of mass M and radius a and a massless stem is
placed on an inclined plane that makes an anale a with
O D
8
00
w3 (t)
FB
= Wx
H
9
[12(12-11)
13(13-11).
12 (121) sech(1/7).
F9
1/2
0
F10
P
11
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