Implicit one-step dynamic algorithms with configuration-dependent parameters: application to central force fields
This work presents a family of implicit one-step algorithms for non-linear dynamics possessing the ability to conserve some of the integrals of the underlying Hamiltonian motion. Algorithmic parameters, normally taken as constants, are here made dependent on the actual configuration and thus become...
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| Veröffentlicht in: | Meccanica (Milan) Jg. 51; H. 6; S. 1321 - 1341 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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01.06.2016
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| ISSN: | 0025-6455, 1572-9648 |
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| Abstract | This work presents a family of implicit one-step algorithms for non-linear dynamics possessing the ability to conserve some of the integrals of the underlying Hamiltonian motion. Algorithmic parameters, normally taken as constants, are here made dependent on the actual configuration and thus become particularly suitable for capturing some of the additional properties of a non-linear motion, while at the same time not increasing the computational burden in the Newton–Raphson solution process. The family of algorithms presented includes several well-known implicit algorithms as special cases. The idea is presented on a two-degree-of-freedom problem of a point mass moving in a central force field. The concept is illustrated on two model examples taken to represent some of the issues in non-linear elastodynamics and celestial mechanics: a stiff mechanical problem and a problem possessing an additional integral of motion. It is shown that in this way overall motion of a stiff problem may be described much better even using very large time steps while, for the Keplerian motion, the anomalous perihelion drift may be successfully removed. |
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| AbstractList | This work presents a family of implicit one-step algorithms for non-linear dynamics possessing the ability to conserve some of the integrals of the underlying Hamiltonian motion. Algorithmic parameters, normally taken as constants, are here made dependent on the actual configuration and thus become particularly suitable for capturing some of the additional properties of a non-linear motion, while at the same time not increasing the computational burden in the Newton–Raphson solution process. The family of algorithms presented includes several well-known implicit algorithms as special cases. The idea is presented on a two-degree-of-freedom problem of a point mass moving in a central force field. The concept is illustrated on two model examples taken to represent some of the issues in non-linear elastodynamics and celestial mechanics: a stiff mechanical problem and a problem possessing an additional integral of motion. It is shown that in this way overall motion of a stiff problem may be described much better even using very large time steps while, for the Keplerian motion, the anomalous perihelion drift may be successfully removed. |
| Author | Jelenić, Gordan |
| Author_xml | – sequence: 1 givenname: Gordan surname: Jelenic fullname: Jelenic, Gordan |
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| Cites_doi | 10.1002/cpa.3160310205 10.1007/BF01881678 10.1007/BF02440162 10.1016/0045-7825(96)01009-2 10.1007/BF01396331 10.1016/S0045-7825(00)00256-5 10.1098/rsta.1999.0366 10.1016/0375-9601(88)90773-6 10.1063/1.532892 10.1002/1097-0207(20001210)49:10<1295::AID-NME993>3.0.CO;2-W 10.1016/j.cma.2007.04.002 10.1016/S0168-9274(97)00061-5 10.1002/nme.1620380903 10.1017/CBO9780511608797 10.1088/0305-4470/39/19/S04 10.1002/zamm.200700173 10.1143/PTP.37.798 10.1002/nme.1620371108 10.1007/BF00913408 10.1137/090771648 10.1007/s00466-011-0570-0 10.1002/cnm.520 10.1007/978-3-642-58360-5_15 10.1002/1097-0207(20001020)49:5<599::AID-NME960>3.0.CO;2-9 10.1016/j.physd.2008.11.014 10.1016/S0045-7825(01)00283-3 10.1007/BF02430634 10.1016/j.cma.2005.07.025 10.1016/S0167-2789(97)00051-1 10.1007/s10208-008-9030-4 10.1016/S0045-7825(03)00366-9 10.1007/978-1-4757-2063-1 10.1023/A:1019127111709 10.1007/s11044-007-9043-9 10.1002/nme.1620310103 10.1016/0898-1221(94)00236-E 10.1016/0045-7825(92)90115-Z 10.1515/crll.1965.218.204 10.1007/978-3-642-05221-7 10.1115/1.4001388 10.1007/978-1-4899-3093-4 |
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| Keywords | Laplace–Runge–Lenz vector Non-linear configuration-dependent integration parameters Conserving time integration Relative equilibria Kepler’s problem |
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| SubjectTerms | Algorithms Automotive Engineering Civil Engineering Classical Mechanics Elastodynamics Integrals Mathematical models Mechanical Engineering Nonlinear dynamics Nonlinearity Parameters Perihelions Physics Physics and Astronomy |
| Title | Implicit one-step dynamic algorithms with configuration-dependent parameters: application to central force fields |
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