Non-linear oscillations of third order systems

... fu n c tio n s A l , B i, Uị f r o m (1 ), w c firs t e x p a n d R q in th e F o u r ie r series: Nonlinear oscillations o f third order systems Part I 513 00 ( ) [ g , ( a ) c o s « 9> + /i„(a)sin ... u a tio n o f the syste m (1 ) a s : (1. 14) (a ) dt Obviously, the stability condition of the stationary solution a = a0y &(ơ0) = (1. 14) is of the form: ' ( a o) < (1 ) Th...

Ngày tải lên: 08/04/2015, 15:29

... equation of the re­ sonance curve: (3.3) w h ere w e deno te (3 ) T h e firs t s ta b ility c o n d itio n (2 ) is o f the f o r m : - yp a l > , Nonlinear oscillations o f third order systems Part II ... purpose, we represent the solution of Eq (4.1) in the form: (5 ) X =* a0cos(yt + ip0)+ b Q o sQ t9 131 Nonlinear oscillations o f third order systems Part II...

Ngày tải lên: 08/04/2015, 15:29

... r v e d on n n a lo ''- c o m p u te r t o o fig r Non-autonomous Systems (continued) Parametric Ocnillotion of third order non-linear System ?he f o llo w in g e q u a tio n i X - Q2 X + l a ... ( ) i n t h e f i r s t a p p r o x im a ­ - - • 519 - The stability condition of the stationary solution ia of form + i r 21) ] > , > Rz-px^ For the D u ffin g case (2.6) v/e h a v e t...

Ngày tải lên: 08/04/2015, 15:30

... Dao B \ contrast with the parametric oscillation in the well k n ow n second -order system , ie riiidity o f the nonlin ear system and the m ax im u m o f the am plitudes o f oscillation ĩr e te ... m= [ qm( a ) c o s m ( p + p m(a )s i nm (p ] , - / o + ữcos^ ccos Nonlinear oscillations o f the third order systems Part III 255 lere 2.71 q0 = — Ị f i a c o s q )...

Ngày tải lên: 08/04/2015, 15:29

... Cite this article as: El-Sayed and Gaafar: Stability of a nonlinear non-autonomous fractional order systems with different delays and non-local conditions Advances in Difference Equations 2011 ... differential-difference equations J Frac Calculus 10, 101–107 (1996) El-Sayed, AMA, Gaafar, FM, Hamadalla, EMA: Stability for a non-local non-autonomous system o...

Ngày tải lên: 20/06/2014, 22:20

... done for nonoscillation of all solutions of nonlinear functional differential equations In this connection, Parhi 10 established some sufficient conditions for oscillation of all solutions of the ... non-oscillation of solutions of some nonlinear differential equations of third order,” ¸ Nonlinear Dynamics and Systems Theory, vol 7, no 4, pp 419–430, 2007 2...

Ngày tải lên: 22/06/2014, 02:20

... where y, z ∈ P and y ≤ τ x , z ≤τ x Boundary Value Problems 3 Singular Third-Order Boundary Value Problem This section discusses singular third-order boundary value problem 1.1 Let P {x ∈ C I ... “Positive solutions of singular third-order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol 306, no 2, pp 589–603, 2005...

Ngày tải lên: 21/06/2014, 05:20

... system was integer and has no interval uncertainty To the best of our knowledge, stabilization of fractional-order open-loop systems with interval uncertainties via fractional-order controllers ... uncertain fractional-order nonlinear systems with interval Jacobian matrix Robust Stability of FO-LTI Interval System From previous section, for the robust sta...

Ngày tải lên: 21/06/2014, 16:20

... budget on HDD servo systems, and hence more demanding tasks with the modeling and control design This calls for a more careful study of the dynamic characteristics of HDD servo mechanism and further ... towards modeling and compensation of friction and nonlinearities in HDD servo systems These are the main points of this chapter In the next chapter, or C...

Ngày tải lên: 15/09/2015, 22:15

... which is a monotone positive solution of the BVP 1.3 Theorem 3.2 If H1 f ∞ < < H2 f0 , then the BVP 1.3 has at least one monotone positive solution Proof The proof is similar to that of Theorem ... x y ∈ 0, ∞ , then the BVP 1.3 has no monotone positive solution 10 Boundary Value Problems Proof Suppose on the contrary that u is a monotone positive solution...

Ngày tải lên: 21/06/2014, 11:20

... coefficients of the differential operators of System 1.1 are nonlinear and that they may not necessarily be bounded from P Cerda and P Ubilla below by a positive bound which is independent of u and v ... by FONDECYT, Grant no 1040990 7.2 P Cerda and P Ubilla References D G de Figueiredo and P Ubilla, “Superlinear systems of second-order ODE’s,” to appear in Nonlinear...

Ngày tải lên: 22/06/2014, 06:20

... coefficients of the differential operators of System 1.1 are nonlinear and that they may not necessarily be bounded from P Cerda and P Ubilla below by a positive bound which is independent of u and v ... by FONDECYT, Grant no 1040990 7.2 P Cerda and P Ubilla References D G de Figueiredo and P Ubilla, “Superlinear systems of second-order ODE’s,” to appear in Nonlinear...

Ngày tải lên: 22/06/2014, 19:20

... ACTA MATHEMATICA VIETNAMlCA TO M 3, N ° (1978) P aram etric oscillations of dynamical system s with cubic term at the modulation depth under the influence of nonlinear frictions N G U ... later the nonlinearity of the system under consider­ ation/coefficient a/stron gly influences to the maximum of am plitudes of stationary oscillations and thei...

Ngày tải lên: 08/04/2015, 15:30

... PỈUVLEEDINGS OF ĩỉìli NATIONAL CENTI M echanics Asym ptotic method for investigation of m u i t if r e q u e n c y oscillations of q u a silin e a r systems of second o r d e r NGUYEN Institute VAN of ... I960 (j Ngu ven V a n Đao, Nguven Van Đinh, A sv m p lo íic method fo r tho q u a s ilin c a r system s or sccond order P roceedings of Hanoi P olvlechnical I n s...

Ngày tải lên: 08/04/2015, 15:36

... Yakar et al.: Boundedness and Lagrange stability of fractional order perturbed system related to unperturbed systems with initial time difference in Caputo’s sense Advances in Difference Equations ... notions of boundedness and Lagrange stability are with respect to the null solution, but initial time difference boundedness and...

Ngày tải lên: 20/06/2014, 22:20