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Generalized Lagrange’s equations for systems with general constraints and distributed parameters
Multibody System Dynamics ( IF 3.4 ) Pub Date : 2019-10-02 , DOI: 10.1007/s11044-019-09706-z
Samir A. Emam

This paper presents a general explicit differential form of Lagrange’s equations for systems with hybrid coordinates and general holonomic and nonholonomic constraints. The appropriate constraint conditions are imposed on d’Alembert–Lagrange principle via Lagrange multipliers to find the correct equations of state of nonholonomic systems. The developed equations take the differential form in terms of the Lagrangian, accounting for the masses and springs that may exist at the boundary. The Lagrangian of hybrid-coordinate systems consists of three parts: the first is due to the rigid-body motion, the second is due to the boundary elements, and the third is the Lagrangian density due to the elastic elements. The developed Lagrange’s equations produce the equations of state and the boundary conditions without the need to carry out the integration by parts generally one needs to do using Hamilton’s principle. Illustrative examples are introduced to show the effectiveness of the developed equations.

中文翻译:

具有一般约束和分布参数的系统的广义拉格朗日方程

本文介绍了具有混合坐标以及一般完整和非完整约束的系统的Lagrange方程的一般显式微分形式。通过拉格朗日乘子对d'Alembert-Lagrange原理施加适当的约束条件,以找到非完整系统的正确状态方程。所开发的方程式采用拉格朗日方程的微分形式,说明了边界处可能存在的质量和弹簧。混合坐标系的拉格朗日分三部分组成:第一部分是由于刚体运动引起的,第二部分是由于边界元素引起的,第三部分是由于弹性元素引起的拉格朗日密度。所开发的拉格朗日方程产生状态方程和边界条件方程,而无需进行零件积分,通常需要使用汉密尔顿原理进行零件积分。引入说明性示例以说明所开发方程的有效性。
更新日期:2019-10-02
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