ABSTRACT The main idea of the structure-preserving method is to preserve the intrinsic geo- metric properties of the continuous system as much as possible in numerical algorithm design. The geometric constraint in the...ABSTRACT The main idea of the structure-preserving method is to preserve the intrinsic geo- metric properties of the continuous system as much as possible in numerical algorithm design. The geometric constraint in the multi-body systems, one of the difficulties in the numerical methods that are proposed for the multi-body systems, can also be regarded as a geometric property of the multi-body systems. Based on this idea, the symplectic precise integration method is applied in this paper to analyze the kinematics problem of folding and unfolding process of nose under- carriage. The Lagrange governing equation is established for the folding and unfolding process of nose undercarriage with the generalized defined displacements firstly. And then, the constrained Hamiltonian canonical form is derived from the Lagrange governing equation based on the Hamil- tonian variational principle. Finally, the symplectic precise integration scheme is used to simulate the kinematics process of nose undercarriage during folding and unfolding described by the con- strained Hamiltonian canonical formulation. From the numerical results, it can be concluded that the geometric constraint of the undercarriage system can be preserved well during the numerical simulation on the folding and unfolding process of undercarriage using the symplectic precise integration method.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11672241,11372253 and 11432010)the Shanxi National Science Foundation(No.2015JM1026)+3 种基金the Astronautics Supporting Technology Foundation of China(No.2015-HT-XGD)111 Project(No.B07050) to the Northwestern Polytechnical Universitythe fund of the State Key Laboratory of Solidification Processing in NWPU(No.SKLSP201643)the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(No.GZ1605)
文摘ABSTRACT The main idea of the structure-preserving method is to preserve the intrinsic geo- metric properties of the continuous system as much as possible in numerical algorithm design. The geometric constraint in the multi-body systems, one of the difficulties in the numerical methods that are proposed for the multi-body systems, can also be regarded as a geometric property of the multi-body systems. Based on this idea, the symplectic precise integration method is applied in this paper to analyze the kinematics problem of folding and unfolding process of nose under- carriage. The Lagrange governing equation is established for the folding and unfolding process of nose undercarriage with the generalized defined displacements firstly. And then, the constrained Hamiltonian canonical form is derived from the Lagrange governing equation based on the Hamil- tonian variational principle. Finally, the symplectic precise integration scheme is used to simulate the kinematics process of nose undercarriage during folding and unfolding described by the con- strained Hamiltonian canonical formulation. From the numerical results, it can be concluded that the geometric constraint of the undercarriage system can be preserved well during the numerical simulation on the folding and unfolding process of undercarriage using the symplectic precise integration method.
