力学系统的二阶梯度表示

物理学报

力学系统的二阶梯度表示

楼智美, 梅凤翔. 2012: 力学系统的二阶梯度表示, 物理学报, 61(2): 337-340.

引用本文:

楼智美, 梅凤翔. 2012: 力学系统的二阶梯度表示, 物理学报, 61(2): 337-340.

2012: A second order gradient representation of mechanics system, Acta Physica Sinica, 61(2): 337-340.

Citation:

2012: A second order gradient representation of mechanics system, Acta Physica Sinica, 61(2): 337-340.

A second order gradient representation of mechanics system

摘要: 研究力学系统运动微分方程的梯度表示以及二阶梯度表示.将完整和非完整力学系统的微分方程在正则坐标下表出.给出系统成为梯度系统以及二阶梯度系统的条件.举例说明结果的应用.
- 完整力学系统 /
- 非完整力学系统 /
- 梯度
Abstract: A gradient representation and a second order gradient representation of the mechanics system are studied.The differential equations of motion of the holonomic and nonholonomic mechanics systems are expressed in the canonical coordinates.A condition under which the system can be considered as a gradient system is given.A condition under which the system can be considered as a second order gradient system is obtained.Two examples are given to illustrate the application of the result.