Deterministic and stochastic algorithms for mechanical systems under constraints
We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of a...
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Published in | Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences Vol. 362; no. 1821; pp. 1583 - 1594 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
England
The Royal Society
15.08.2004
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Subjects | |
Online Access | Get full text |
ISSN | 1364-503X 1471-2962 |
DOI | 10.1098/rsta.2004.1400 |
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Abstract | We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations. |
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AbstractList | We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations. We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non–Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time–dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations. We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations.We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems subject to constraints. We also show how all this is related to the treatment of general non-Hamiltonian systems. Then we introduce a family of algorithms derivable from approximations of the evolution operator obtained via the Trotter formula. Generalizing the treatment to time-dependent force fields we also show how one can adapt those algorithms to ordinary stochastic differential equations. |
Author | Giovanni Ciccotti Galina Kalibaeva |
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Cites_doi | 10.1209/epl/i1999-00139-0 10.1007/978-3-540-39895-0_5 10.1090/S0002-9939-1959-0108732-6 10.1063/1.463137 10.1080/00268979600100761 10.1063/1.434317 10.1063/1.444728 10.1063/1.1378321 10.2183/pjab.69.161 10.1103/PhysRevE.61.6165 10.1080/0026897031000108113 10.1016/0167-7977(86)90022-5 10.1103/PhysRevB.17.1302 |
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equations of motion for systems... We discuss the general philosophy underlying the statistical behaviour, the dynamical evolution and the integration of the equations of motion for systems... |
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SubjectTerms | Algorithms Atoms Conservation laws Differential equations Dynamical systems Equations of motion Holonomic Constraints Mathematical expressions Molecular dynamics Molecules Non-Hamiltonian And Brownian Dynamics Statistical mechanics Trajectories |
Title | Deterministic and stochastic algorithms for mechanical systems under constraints |
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