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循环积分     
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  cyclic integral
     This paper studies integration theory for Vacco dynamical equation of nonlinear nonholonomic system. First, the first integrals of Vacco equation are given. Secondly, using cyclic integral and energy integral respectively, the order of Vacco equation is reduced, generalized Routh equation and generalized whittaker equation of Vacco form are obtained.
     本文建立非线性非完整系统Vacco动力学方程的积分理论,由Vacco方程给出系统的第一积分,分别利用循环积分和能量积分降阶Vacco型方程,得到Vacco型广义Routh方程和广义Whittaker方程,建立了Vacco型正则方程和变分方程,并由第一积分构造系统的一类积分不变量,最后,给出其Poincare-Cartan型、Poincare型积分变量关系和积分不变量。
短句来源
     Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively.
     其次,分别利用系统的循环积分、能量积分降阶运动方程,得到推广的Routh方程和推广的Whittaker方程;
短句来源
     By using higher order Lagrange equations of holonomic mechanical system,higher order Hamilton's canonical equations of holonomic mechanical system are obtained,by which the higher order cyclic integral and the higher order generalized energy integral of holonomic potential mechanical system are obtained,and the physical meaning of higher order Hamilton's function is explained.
     运用完整力学系统的高阶Lagrange方程建立了完整力学系统的高阶Ham ilton正则方程,得到完整有势力学系统高阶循环积分和高阶广义能量积分,并阐明了高阶Ham ilton函数的物理意义.
短句来源
     Motivated by concepts of Jacobi integral and cyclic integral in analytical me-chanics and energy-momentum tensor in electro-magntic field,the conservation laws forpiezoelectric materials were derived, from which the path independent integrals can be ob-tained.
     借鉴分析动力学中的Jacobi积分和循环积分概念,以及电磁场理论中的能量矩概念,导出了压电介质在静态场中的守恒方程形式,由这些守恒方程即可得到在位错、断裂力学和其他缺陷理论中应用广泛的路径无关积分。
短句来源
     On this basis, the higher order Lagrange function is introduced,the higher order Lagrange equations of holonomic potential mechanical system are derived, and the higher order cyclic integral and the integral of higher order generalized energy of the system are obtained.
     在此基础上,引入高阶Lagrange函数,得出完整有势力学系统的高阶Lagrange方程,并得到系统高阶循环积分和高阶广义能量积分.
短句来源
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  cycle integrals
     The Cycle Integrals of Lagranges Equations for Nonconservative Systems and Their Applications
     非保守系统Lagrange方程的循环积分形式及其应用
短句来源
     For nonconservative systems, the cycle integrals of Lagranges equations which represent the theorems of generalized impulse are deduced, and the calculation methods of generalized impulse are also given, so that a new way of application is provided for Lagranges equations.
     给出了非保守系统Lagrange方程的循环积分形式,同时指出其代表了广义冲量定理,并给出了广义冲量的计算方法,从而为Lagrange方程提供了新的应用途径.
短句来源
  cycle integrating
     A succinct expression and cycle integrating on the sum of equal powers are obtained here and the value of the formula S 1(N)~S 111 (N) is given.
     获得了等幂和的简洁表示及其循环积分公式 ,得到了Bernoulli数B0 ~B110 及等幂和公式S1(n)~S111(n)的值 .
短句来源
     In this paper, the sum of equal powers is discussed. Bernowlli's numbers B72-B100and the cycle integrating formula are obtained. 107 expressions on the sum of equal powers are given by the formula above, and calculate formula of M-N expression on the sum of equal powers is obtained.
     讨论了等幂和问题,求出了B_(72)~B_(100)的值,得到了等幂和的循环积分公式,利用它们可求得等幂和的前107个公式,并得到了等幂和的M-N表示法的计算公式。
短句来源
  cyclic integrals
     Based on the generalized Routh equation and generalized chaptygin equation of relativistic nonlinear nonholonomic system, the generalized cyclic integrals, generalized energy integrals and local energy integrals and their conditions of existence for the system are gived. The former conclasion for the first integrals of holonomic system and classical mechanics system are special cases in this paper.
     分别从相对论性非线性非完整系统的广义 Routh方程、广义лигин方程出发,研究这类系统的广义循环积分、广义能量积分和局部能量积分存在的条件,以往关于第一积分的研究结果均为本文的特款.
短句来源
     Secondly,the order of the equation of motion is reduced by using cyclic integrals and energy integrals,and thus the generalized Routh equation and generalized Whittaker equation are obtained. Thirdly,the canonical equation and variational equation of the system are established,and the integral invariant is constructed by using the first integrals.
     给出系统运动的第一积分 ,分别利用系统的循环积分和能量积分降阶运动方程 ,得到推广的Routh方程和推广的Whittaker方程 ,建立系统运动的正则方程和变分方程 ,并由第一积分构造系统的积分不变量 .
短句来源
     The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
     结果显示 :Birkhoff系统存在广义能量积分和循环积分 ,每个积分可使Birkhoff系统降两阶
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  cyclic integral
Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively.
      
The problem of motion of a dynamically symmetric gyrostat acted upon by non-symmetric potential forces admitting a cyclic integral is considered.
      
  cycle integrals
p-Adic congruences for cycle integrals associated to elliptic curves with complex multiplication
      
  cyclic integrals
The moments of this distribution are simple combinations of cyclic integrals of the potential function.
      
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