دورية أكاديمية

Matrix Equations of the Motion of Multibody Systems with a Tree Structure in Hamiltonian Variables

التفاصيل البيبلوغرافية
العنوان: Matrix Equations of the Motion of Multibody Systems with a Tree Structure in Hamiltonian Variables
المؤلفون: Vladimir Ivanov, Vladimir Shimanovskiy
المصدر: Journal of Applied and Computational Mechanics, Vol 9, Iss 4, Pp 1107-1121 (2023)
بيانات النشر: Shahid Chamran University of Ahvaz, 2023.
سنة النشر: 2023
المجموعة: LCC:Mechanics of engineering. Applied mechanics
مصطلحات موضوعية: multibody system, equations of motion, dynamics, mathematical modeling, generalized coordinates, poisson momenta, Mechanics of engineering. Applied mechanics, TA349-359
الوصف: The paper develops the methods for computer simulation of the dynamics of absolutely rigid body systems with a tree structure. The equations of motion are presented in compact matrix form. The case of holonomic constraints is also considered. Since the independent parameters uniquely determine the positions and velocities of the bodies of the system in space, the generalized coordinates and variables with the dimension of impulses are chosen. A feature of the system of equations is that it is resolved with respect to the derivatives of the generalized momenta and does not contain constraint reactions. The derivation of the proposed form of the equations of motion from the Hamilton principle using the matrix-geometric approach is given. Recursive formulas for determining all kinematic and dynamic variables included in the equations are obtained. As an example of a mechanical system with six degrees of freedom, all stages of preparing primary information and compiling equations of motion in the proposed form are demonstrated. Three algorithms are presented that allow resolving the obtained extended system of equations with respect to the generalized velocities and momenta without direct formation of the Hamilton equations. The classification of the equations of motion of rigid body systems is carried out from their structure point of view. The place of the deduced equations in the general classification is also demonstrated. A comparative analysis of the computational complexity of the considered methods for various classes of mechanical systems is carried out. Some diagrams are constructed that allow choosing the most effective modeling method depending on the characteristics of the mechanical system: the number of bodies, the number of degrees of freedom and the structure of the system.
نوع الوثيقة: article
وصف الملف: electronic resource
اللغة: English
تدمد: 2383-4536
العلاقة: https://jacm.scu.ac.ir/article_18327_e710e9ca75a0e66ab55ac54a1a5aca2e.pdfTest; https://doaj.org/toc/2383-4536Test
DOI: 10.22055/jacm.2023.42102.3872
الوصول الحر: https://doaj.org/article/475a53f2149241398a3d172f91bbd6eeTest
رقم الانضمام: edsdoj.475a53f2149241398a3d172f91bbd6ee
قاعدة البيانات: Directory of Open Access Journals
الوصف
تدمد:23834536
DOI:10.22055/jacm.2023.42102.3872