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31.
The surfaces of section in a harmonic oscillator potential, perturbed by quartic terms, are obtained analytically. A succession
of action‐angle, Lissajous and Lie transformations near the 1:1 commensurability, reduces the three‐dimensional motion to
a one‐dimensional one. The latter is solved in terms of Jacobi's elliptic functions. Existence conditions for periodic orbits
are found and two general families of such solutions are introduced. Two examples of regular motions in oblate and prolate
spheroids are discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
32.
33.
New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k
2)1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia 相似文献
34.
Akmal A. Vakhidov 《Celestial Mechanics and Dynamical Astronomy》2001,81(3):177-190
A new system of recurrence relations for Hansen coefficients is obtained. This system gives a connection between only those coefficients which are included in the disturbing function of planetary or satellite motion and allows to compute efficiently the Hansen coefficients for perturbations both from internal and external bodies. The recurrence process can be realized both from high to low and from low to high harmonical terms of the disturbing function. The corresponding algorithms of evaluation of Hansen coefficients are presented. The efficiency of the obtained system of recurrence relations is discussed. 相似文献
35.
A symplectic mapping for Trojan-type motion has been developed in the secularly changing elliptic restricted three-body problem. The mapping describes well the characteristics of Trojan-type dynamics at small eccentricities. By using this mapping the boundary of the stability region has been studied for different values of the initial eccentricities of hypothetical Jupiter's Trojans. It has been found that in the secularly changing elliptic case the chaotic diffusion at the border of the stability region is stronger than simply in the elliptic case. An explanation of this observation might be the destruction of the chain of islands of the 13:1 secondary resonance between the short and long period component of the Trojan-like motion, caused possibly by the indirect perturbations of Saturn. 相似文献
36.
A new fair off-line electronic cash scheme on elliptic curve cryptography was presented. The new scheme is more efficient than those by extending fair off-line electronic cash scheme from finite field into elliptic curve cryptography and introducing a new elliptic curve discrete logarithm assumption. The expiry date and denomination are embedded into the blindly signed coin by integrating partially blind signature with restrictive blind signature. A bank need not use different public keys for different coin values, shops and users need not carry a list of bank's public keys to verify in their electronic wallet. At the same time, the bank just needs to keep undue electronic coins for double spending check in his database, thus bank's database can be dramatically reduced. 相似文献
37.
利用复变函数法和Green函数法给出了SH波对垂直界面附近椭圆形夹杂散射问题的解析解答。首先,将待求的半空间模型沿垂直边界分割为区域Ⅰ和区域Ⅱ两个直角域。通过保角映射的方法将区域Ⅰ内椭圆形夹杂的外域映射为单位圆外域,并利用镜像方法构造出两个区域内满足直角域边界条件的散射波场及适用的Green函数;其次,利用界面契合思想,通过在界面处添加附加力系的方法建立起满足界面处位移和应力连续条件的无穷代数方程组,并截断有限项求解;最后,给出了求解地表位移幅值的具体算例。结果表明,入射波数、入射角度、夹杂位置、垂直界面以及材料参数都对地表位移幅值的分布有影响。 相似文献
38.
Bruce R. Miller 《Celestial Mechanics and Dynamical Astronomy》1991,51(3):251-270
We examine a parametric family of cubic perturbed 1-1 resonant harmonic oscillators with an aim to understanding the phase flows of the reduced system. Variation of the parameters leads the system through five bifurcations of different types. Some bifurcations are due to passage through cases of discrete symmetry or integrability. A conjecture correlating degenerate equilibria in reduced systems with integrability is modified and reinforced. 相似文献
39.
本文利用等量坐标与等角投影之间的关系,以Guyou椭圆坐标为例,求得其等量坐标,并进一步导出相应的等角投影方程。该方法为新投影的探求,开辟了广阔的前景。 相似文献
40.
The implicit nonlinear normal mode initialization (INMI) is applied to a tropical limited area shallow water model in spherical coordinates.The boundary condition for the INMI scheme is based on the boundary formulation of the model.The INMI scheme is found to be very efficient in suppressing spurious gravity wave oscillation and providing a well balanced initial data set for the model.The INMI scheme involves solving a number of elliptic type equations with varying complexity.and hence an efficient numerical technique is required for solving such equations.In order to make INMI computationally more attractive,we are employing the multigrid method for solving all the elliptic type equations in the INMI scheme.The numerical procedures for the development of such multigrid solvers are briefly described. 相似文献