caa a22 4500 445360534 CHVBK 20180317142913.0 cr unu---uuuuu 170323e20110401xx s 000 0 eng 10.1007/s11071-010-9849-5 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9849-5 Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism [Elektronische Daten] [Taeyoung Lee, Melvin Leok, N. McClamroch] A high fidelity model is developed for an elastic string pendulum, one end of which is attached to a rigid body while the other end is attached to an inertially fixed reel mechanism which allows the unstretched length of the string to be dynamically varied. The string is assumed to have distributed mass and elasticity that permits axial deformations. The rigid body is attached to the string at an arbitrary point, and the resulting string pendulum system exhibits nontrivial coupling between the elastic wave propagation in the string and the rigid body dynamics. Variational methods are used to develop coupled ordinary and partial differential equations of motion. Computational methods, referred to as Lie group variational integrators, are then developed, based on a finite element approximation and the use of variational methods in a discrete-time setting to obtain discrete-time equations of motion. This approach preserves the geometry of the configurations, and leads to accurate and efficient algorithms that have guaranteed accuracy properties that make them suitable for many dynamic simulations, especially over long simulation times. Numerical results are presented for typical examples involving a constant length string, string deployment, and string retrieval. These demonstrate the complicated dynamics that arise in a string pendulum from the interaction of the rigid body motion, elastic wave dynamics in the string, and the disturbances introduced by the reeling mechanism. Such interactions are dynamically important in many engineering problems, but tend be obscured in lower fidelity models. The Author(s), 2010 Lagrangian mechanics nationallicence Geometric integrator nationallicence Variational integrator nationallicence String pendulum nationallicence Reel mechanism nationallicence Rigid body nationallicence Lee Taeyoung Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, 32901, Melbourne, FL, USA aut Leok Melvin Department of Mathematics, University of California, 92093, San Diego, CA, USA aut McClamroch N. Department of Aerospace Engineering, University of Michigan, 48109, Ann Arbor, MI, USA aut Nonlinear Dynamics Springer Netherlands 64/1-2(2011-04-01), 97-115 0924-090X 64:1-2<97 2011 64 11071 https://doi.org/10.1007/s11071-010-9849-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9849-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lee Taeyoung Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, 32901, Melbourne, FL, USA aut NATIONALLICENCE 700 1- Leok Melvin Department of Mathematics, University of California, 92093, San Diego, CA, USA aut NATIONALLICENCE 700 1- McClamroch N. Department of Aerospace Engineering, University of Michigan, 48109, Ann Arbor, MI, USA aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 64/1-2(2011-04-01), 97-115 0924-090X 64:1-2<97 2011 64 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer