Development of an efficient formulation for Volterra’s equations of motion for multibody dynamical systems
نویسندگان
1 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Department of Civil Engineering, Faculty of Science &Technology, Abbes Laghrour University, Khenchela, Algeria.
2 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Department of Civil Engineering, Faculty of Science &Technology, Abbes Laghrour University, Khenchela, Algeria.
3 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Department des Sciences et de la Technologie, Universite de Tissemsilt, Hamouda, Algerie
4 Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria
5 - Department of Civil Engineering Material and Hydrology Laboratory, Faculty of Technology, University of Sidi Bel Abbes, Khenchela, Algeria. - Yonsei Frontier Lab, Yonsei University, Seoul, Korea. - Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Eastern Province, Saudi Arabia. - Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia.
6 Department of Mathematics, Govt. College University Faisalabad, Faisalabad, Pakistan
doi
10.24200/sci.2024.60600.6891چکیده
In this paper, we present an efficient form of Volterra’s equations of motion for both unconstrained and constrained multibody dynamical systems that include ignorable coordinates. The proposed method is applicable for systems with both holonomic and nonholonomic constraints. Firstly, based on the definition of ignorable coordinates, one of the motion constants (the generalized momentum vector corresponding to the ignorable coordinates) is considered as a constraint, which will be referred to as dynamical constraints. These constraints, along with ordinary constraints, namely kinematical constraints, are then used in the proposed method to derive motion equations. This approach gives the minimum number of equations needed to study the behavior of a dynamical system. Three simulation examples are provided to evaluate the proposed method and to compare it to existing methods. The first case study is a constrained dynamical system, which moves in two-dimensional space. The second one is an unconstrained multibody system including three connected rigid bodies. Finally, the last case study includes a cubic satellite that uses a deployable boom to move a mass to a desired location. The results of the numerical simulations are compared to the conventional methods and the better performance of the proposed method is demonstrated.
