【作者】 王亮；

【导师】 史东华；

【作者基本信息】 北京理工大学 ， 应用数学， 2016， 硕士

【摘要】 Hamel形式是通过引入非物质速度对Lagrange力学的一般表示.Hamel场变分积分子是利用场论下的Hamel形式提出的变分积分子,该离散方式在保持无穷维力学系统定性性质方面有优良表现,可以广泛应用于带约束的无穷维力学系统,尤其是带非完整约束的力学系统.本文对于几何精确梁的模型,通过Hamel场形式得到几何精确梁的动力学方程,然后利用Hamel场变分积分子给出几何精确梁的离散运动方程.文章最后通过两个数值仿真说明,该数值形式具有长时间保持能量、动量和几何结构的特点.更多还原

【Abstract】 Hamel’s formalism is a general representation of Lagrange mechanics by introduc-ing non-material velocity.Hamel field variational integrators are derived in Hamel’s formalism for field theories,which have good performance in preserving qualitative properties of infinite dimensional mechanical systems and can be widely applied to con-strained systems,especially those with nonholonomic constraints.In this paper,the geometrically exact beam dynamics are derived by using the Hamel field formalism,and then the discrete form of the geometrically exact beam is given by the Hamel field variational integrators.Finally,two simulations illustrates that the derived algorithm preserves energy,momentum and geometry structure in exponentially long time.更多还原