Applied Mathematics and Mechanics (English Edition) ›› 1993, Vol. 14 ›› Issue (10): 907-918.

• 论文 • 上一篇    下一篇

INTEGRAL THEORY FOR THE DYNAMICS OF NONLINEAR NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

罗绍凯   

  1. Shangqiu Normal College, He’nan
  • 收稿日期:1992-09-09 出版日期:1993-10-18 发布日期:1993-10-18
  • 基金资助:
    Project supported by the Natural Science Foundation of He’nan Province

INTEGRAL THEORY FOR THE DYNAMICS OF NONLINEAR NONHOLONOMIC SYSTEM IN NONINERTIAL REFERENCE FRAMES

Luo Shao-kai   

  1. Shangqiu Normal College, He’nan
  • Received:1992-09-09 Online:1993-10-18 Published:1993-10-18
  • Supported by:
    Project supported by the Natural Science Foundation of He’nan Province

摘要: This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively. Thirdly, derives canonical equation and variation equation and by using the first integral constructs integral invariant. And then, establishes the basic integral variants and the integral invariant of Poincare-Cartan type. Finally, we give a series of deductions.

Abstract: This paper establishes the integral theory for the dynamics of nonlinear nonholonomic system in noninertial reference frame. Firstly, based on the Routh equation of the relative motion of nonlinear nonholonomic system gives the first integral of the system. Secondly, by using cyclic integral or energy integral reduces the order of the equation and obtains generalized Routh equation and Whittaker equation respectively. Thirdly, derives canonical equation and variation equation and by using the first integral constructs integral invariant. And then, establishes the basic integral variants and the integral invariant of Poincare-Cartan type. Finally, we give a series of deductions.

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