TABLE OF CONTENTS FOR LYAPUNOV (LIAPOUNOFF) AND POINCARE'S METHODS IN THE THEORY OF NONLINEAR OBCILLATIONS'

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600340022-9
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 3
• Document Creation Date: December 22, 2016
• Document Release Date: August 16, 2011
• Sequence Number: 22
• Publication Date: August 25, 1950
• Content Type: REPORT

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CL/SSIFICATION CONFIDENTIAL C~HFIDEHT~AE
CENTRAL INTELLIGENCE AGENCY REPORT
INFORMATION FROM
FOREIC3N DOCUMENTS OR RADIO BROADCASTS CD !':O.
DATE
Scientific -Physics, nonlinear mechanics.
PUBLISHED 191-9
7. Close of Resonance
8. Resonance of the n-th Kind
TABLE OF CONTEPT3 FGR
"LYAPUNOV (LSAPOUNOFF AND POINCARE'8 METHODS IN
THE THEORY OF NOALINEAR OFCII.iATiO1QS
I. G. Makin
P
age
T_~__~_._..~,,.. ~ X
to ervuua. ~i.+++
C
I.
Poincsre's General Theory oP 1eriodic Solutions
1.
Concept oP Poincare's Method. Small Parameters ~
11
2.
3.
Conditions Governing the Existence~of Periodic
Solutions. Poince-re's Theorem
The Case Where the Functional Determinant of the
pei-Functions ~!i Reduce to Zero.
13
15
4.
The Case Where the Differential Equations of Motion do
'~
not Explicitly Con*.ain Time t
The Difficulties that Arise during Practical Aiipli-
DATE OF
INFORMATION 191+9
DATE D13T. ~~ Au8 1950
SUPPLEMEPIT TO
REPORT N0.
- l - ~ON~IDE~~1Al
CONFIDENPIAL
DISTRIBUTION
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Het kYnPunova i Puankare in Teorii Nelinevnvkh Kolebaniy, in the
series, Contemporary Problems of Mechanics, Ogiz, (L C No Q A935 ?M31+)?
sc 35
of Freedom Far from Resonance
Problems Connected with Them
II. Oscillations of Quaeilinear,Systems .
6 0 illations of a N onautonomic System xith One Degree
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CONFIO~~~TlAC
g. Oscillations of a Nonautonomic Quasilinear System
witu At{y Number of Degrees of Freedom Far from
Resonance
10. Close to Resonance
11. Quasilinear Autonomic Systems with One Degree of
Freedom
12. The Phase Plane Yor a Certain System. Limit Cycles.
Auto-oscillations (Self-Induced)
13? Oscillations cf a Quasilinear Autonomic System with
Any Number of Degrees of Freedom.
14. The Defects of a Quasilinear Treatment of Physical
Problems
III. Stability of Periodic Notions
15. Setting up of the Problem. Equations in Jariation 100
16. Linear Equations with Periodic Coefficients. The 104
Characteristic Equation
17.. The Analytic Form of the Solut~~ns 108
18. Lyapunov's Theorem Concerning the Roots of the Char- 119
acteristic Equations of Conjugate Systems
19. Reduction of Equations with Periodic Coefficients 122
to Equations with Constant Coefficients
20. Lyapunov's Theorem on the Stability of Periodic Motions 128
21. Andronov and Kitt's Theorem on the Stability of Periodic 136
-~ -
I~otions oz' AuLUirJl(liti 3y o ~~+'++
22. Approximate Calculation of the Characteristic Indices.
Poincare's Form of the Characteristic Equation 137
23. Criteria oY Stability
142
24. Stability of Oscillations Studied in This Chapter 145
IV. Lyapunov's Theory of Periods: Solutions
25. Lyapunov's Systems
26. Periodic Solutions of I,yapunov's System 154
27. A Practical Method for the Computation of the Periodic ~G9
Solutions of Lyaponov's 5ys:ema
28. Certain Properties of she Periodic Solutions of Lys- 166
punov's Sys+,ems
-2-
CONFIDENT~N~ O61~~p`-~~ tA~.
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CD~~Ip~i~ DIAL
V. Oscillationa of Systems .,rith One Degree of Freedom
that Are Close to I~yapunov's System
43. 'r a rracLices~ ~~~~~?-.,...,_ --- ---- 237
x j)(t)
30.
3l.
32.
Generating Solutions
lf5
Variational Equations of a Generating .System
17i
Conditions Governing the Periodic Sol+ition xn(t), yn(t)
l81
A, Practical Method for the Calculation of the Periodic
Soluticn`xn(t), Yn{t)
185
The Periodic Solution x{?)(t), y(?){t). Resonance
and Nonresonance Cases
193
Oscillations Close to Fesonance
195
A Practical Method for the Calculation of the, Resonance
201
Solution
The Stability of Periodic Solu~ione in 36
204
An Examp'!.e of Application of the Preceding Method
207
224
41. The Periodic Solutions for Resonance
42. The Periodic Solution x(s)(t). Its Existence 232
VI. Oscillations of Systems Kith Many Degrees of Freedom
Which Are Close to Ityapunov's Systems
39 ?' The Generating Solutions
40. The Periodic Solutions x(e)(t)
-3-
cor~tnENTZAt.
_,.: -
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