›› 2014, Vol. 36 ›› Issue (6): 779-782,785.DOI: 10.6052/1000-0879-14-195

• 应用研究 • 上一篇    下一篇

广义坐标形式的高斯最小拘束原理及其推广

姚文莉1, 戴葆青2   

  1. 1. 青岛理工大学理学院, 山东青岛 266520;
    2. 山东科技大学泰山科技学院, 山东泰安 271019
  • 收稿日期:2014-05-26 修回日期:2014-07-23 出版日期:2014-12-15 发布日期:2014-12-17
  • 通讯作者: 姚文莉
  • 基金资助:
    国家自然科学基金资助项目(10872118,11272167).

GAUSS PRINCIPLE OF LEAST CONSTRAINT IN GENERALIZED COORDINATES AND ITS GENERALIZATION

YAO Wenli1, DAI Baoqing2   

  1. 1. College of Science, Qingdao Technological University, Shandong, Qingdao 266520, China;
    2. Taishan College of Science and Technology, Shandong University of Science and Technology, Shandong, Tai'an 271019, China
  • Received:2014-05-26 Revised:2014-07-23 Online:2014-12-15 Published:2014-12-17

摘要: 当采用广义坐标描述系统的运动时,相比质点形式的高斯最小拘束原理,通过广义坐标形式的高斯最小拘束原理来建立动力学优化模型,计算效率更高. 从高斯原理的变分形式出发推导了广义坐标形式的高斯最小拘束原理,并研究了非理想约束、单边约束及刚体碰撞情形下的高斯最小拘束原理的形式. 研究认为:对刚体碰撞情形下,高斯最小拘束原理不能取代碰撞恢复定律,碰撞恢复定律以碰撞后广义速度的约束方程形式起作用.

关键词: 高斯最小拘束原理|广义坐标|优化模型|碰撞

Abstract: When the generalized coordinates are used to describe the motion of a system, a higher computational efficiency will be achieved in using the Gauss principle of least constraint, as compared with in the form of mass points. Based on the Gauss principle in the form of variation, the Gauss principle of least constraint in generalized coordinates is derived. The principle is generalized to cases of non-ideal constraints, unilateral constraints and the collision of rigid body systems. For the collision problem of rigid body systems, it is shown that the collision law cannot be replaced by the Gauss principle of least constraint and it should be used in the form of constraint equations for generalized velocities after collision.

Key words: Gauss principle of least constraint|generalized coordinate|optimization model|collision

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