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101.
102.
This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach. 相似文献
103.
104.
Herein we report a theoretical study on mechanistic photodissociation of glycolaldehyde, HOCH2CHO. Equilibrium structures, transition states, and intersection structures for the α‐C? C and ‐C? H bond fissions and the β‐C? O bond fission in the excited states are determined by the complete active space self‐consistent field (CASSCF) method. Based on the CASSCF optimized structures, the potential energy profiles for the dissociations are refined by performing single‐point calculations using the multi‐state multi‐reference CASSCF second order perturbation (MS‐MR‐CASPT2) method. With a low excitation energy of 280–340 nm, the T1 α‐C? C and β‐C? O bond fissions following intersystem crossing from the S1 state are the predominant and comparable channels, whereas the α‐C? H bond fissions both in the S1 and in the T1 states are nearly prohibited due to the relevant high barriers. The rate constants for the T1 α‐C? C and β‐C? O bond fissions are also calculated by RRKM theory. Furthermore, the S0 reactions can occur as a consequence of intersystem crossing via T1/S0 intersection points resulting from the T1 C? C and C? O bond cleavages. This photodissociation mechanism is consistent with recent experimental studies. 相似文献
105.
Jun Shen 《International Journal of Non》2011,46(9):1177-1190
There exist many types of possible periodic orbits that impact at the walls for the inverted pendulum impacting between two rigid walls. Previous studies only focused on single impact periodic orbits and symmetric periodic orbits that bounce back and forth between the two walls. They respectively correspond to Types I and II orbits in the Chow, Shaw and Rand classification. In this paper we discuss two types of double impact periodic orbits that have not been studied before. The equations need to be solved for double impact orbits are transcendental and it is very hard to see the structure of the solutions. Consequently the analysis of double impact orbits is much more difficult than that of Types I and II orbits. A combination of analytical and numerical methods is employed to investigate the existence, stability and bifurcations of these orbits. Grazing bifurcations, which do not present for Types I and II orbits, are also observed. 相似文献
106.
采用现代计算机图形学、数据库及数字通讯技术,对空中交通管制新航行系统(FANS)的重要组成部分和关键技术进行了初步研究,设计并研制成功了空中交通管制综合显示系统。 相似文献
107.
Kotarski W.; El-Saify H. A.; Bahaa G. M. 《IMA Journal of Mathematical Control and Information》2002,19(4):461-476
A distributed control problem for the parabolic operator withan infinite number of variables and time delay is considered.The performance index has an integral form. Constraints on controlsare imposed. To obtain optimality conditions for the Neumannproblem, the generalization of the DubovitskiiMilyutintheorem given by Walczak in WALCZAK, S. Folia Mathematics, 1,187196 and WALCZAK, S. J. Optim. Theory Appl., 42, 561582was applied. 相似文献
108.
A. I. Karol 《Mathematical Notes》1998,63(1):25-32
We construct the asymptotics ast→0 of the trace of the operator exp(−tP) for an elliptic operatorP on a manifold with conical points.
Translated fromMatematicheskie Zametki, Vol. 63, No. 1, pp. 28–36, January, 1998.
This research was supported by the Belarus Foundation for Basic Research under grant No. 96-01 00790. 相似文献
109.
Karnaukhov V. G. Kozlov V. I. Rasskazov A. O. Karnaukhova O. V. 《Mechanics of Composite Materials》2003,39(1):17-26
Based on the Kirchhoff-Love hypotheses and adequate supplementary hypotheses for the distribution of electric field quantities, a model for parametric vibrations of composite shells of revolution made of a passive (without a piezoeffect) middle layer and two active (with a piezoeffect) surface layers under the action of harmonic mechanical and electric loads is developed. The dissipative material properties are taken into account by linear viscoelastic models. Since the vibrations on the boundary of the main domain of dynamic instability (MDDI) are harmonic, the investigation of this domain, in a first approximation, is reduced to generalized eigenvalue problems, which are solved by the finite-element method. The problem on parametric vibrations of a three-layer conical shell under harmonic mechanical loading is considered. The influence of the shell thickness, dissipation, and electric boundary conditions on the MDDI is investigated. Two limiting cases of electric boundary conditions are considered, where the electrodes are short-circuited or not. The curves presented show a considerable influence of the electric boundary conditions on the characteristics of the MDDI, namely on its width and position on the frequency axis and on the critical parameter of excitation. 相似文献
110.