Abstract
Lie groups and Lie algebras are used to study the recursive dynamics of flexible multi-body systems. First the adjoint transformations and adjoint operators of Lie groups and Lie algebras are discussed. Then the generalized mass matrix of flexible mechanical systems is built on the basis of modal vector. And then the inverse and forward dynamics of flexible mechanical systems are constructed. These two recursive formulas are of high efficient. Finally a four-bar model with flexible body is simulated with above method. The simulation results show that with the method can be solved quickly and efficiently.
Highlights
The mechanical systems are becoming larger in scale and more complex
The assumption of rigid body dynamics has been unable to explain the dynamics of such systems
On the basis of the above methods, this paper describes the dynamics with Lie groups and Lie algebras
Summary
The mechanical systems are becoming larger in scale and more complex. Many kinds of flexible material are used in engineering as members of mechanical systems. Singh establish the equations of tree topology flexible multi-body system dynamics [3]. Shabana use linear and nonlinear finite element method combination of multi-body dynamics theory to establish a flexible body dynamics model [4]. These methods have a problem in dealing with the efficiency and integration method [5]. On the basis of the above methods, this paper describes the dynamics with Lie groups and Lie algebras. It establishes the dynamic equations by recursive methods. It leads to a recursive dynamics of flexible mechanical systems
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