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cyclic integral
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  循环积分
     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.
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  cyclic integral
The problem of motion of a dynamically symmetric gyrostat acted upon by non-symmetric potential forces admitting a cyclic integral is considered.
      
Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively.
      


The condition for the existence of the cyclic integral of the non-holoao-mic conservative systems in the event space is discussed. Using the cyclic integral, the order of the generalized Chaplygin's equations is reduced, and the more generalized Routh's equations are obtained. An example is given.

本文首先讨论事件空间中非完整保守系统存在循环积分的条件,其次利用循环积分将广义方程降阶,得到更广泛一类的Routh方程,最后举例说明新方法的应用。

The relativistic Jourdain's variational principles in velocity space were established, the relativistic generalished Noether's theorm of nonlinear nonholonomic nonpotentlal system were prestented and proved, and relativistic generalized integral and cyclic integral of nonlinear nonholonomic system were obtained. All Noether's theorms and conservation laws of classical mechanics are special cases of this paper.

在速度空间中建立了相对论性Jourdain型变分原理,提出并证明了非线性非完整非有势系统的相对论性广义Noether定理,给出了非线性非完整系统的相对论性广义能量积分和循环积分。经典力学的各种Noether定理和守恒律均是本文结果的特款。

T he Routh equations and the Chaplygin equations for relative motion of nonlinear nonholonomic system are gived, and the cyclic integral and its condition of existence for the system are extended. Using the cyclic integral, the order of the Routh equations and the Chaplygin equations are reduced, and the more generalized Routh equations and the more generalized Routh equations of Chaplygin form are obtained. A seriat of deductions are gived.

本文给出了非线性非完整系统相对运动的Routh方程和方程,得到了具循环积分存在的条件;并利用循环积分将非完整系统相对运动的Routh方程和方程降阶,得到了更广泛一类的广义Routh方程和型广义Routh方程。最后给出一系列推论。

 
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