Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule
We address the design of time integrators for mechanical systems that are explicit in the forcing evaluations. Our starting point is the midpoint rule, either in the classical form for the vector space setting, or in the Lie form for the rotation group. By introducing discrete, concentrated impulses...
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| Format: | Article |
| Language: | English |
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CTU Central Library
2004-01-01
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| Series: | Acta Polytechnica |
| Subjects: | |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/616 |
| _version_ | 1829460868065132544 |
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| author | P. Krysl |
| author_facet | P. Krysl |
| author_sort | P. Krysl |
| collection | DOAJ |
| description | We address the design of time integrators for mechanical systems that are explicit in the forcing evaluations. Our starting point is the midpoint rule, either in the classical form for the vector space setting, or in the Lie form for the rotation group. By introducing discrete, concentrated impulses we can approximate the forcing impressed upon the system over the time step, and thus arrive at first-order integrators. These can then be composed to yield a second order integrator with very desirable properties: symplecticity and momentum conservation. |
| first_indexed | 2024-12-12T11:39:53Z |
| format | Article |
| id | doaj.art-194b111360c84b64a69fe0a7186a6eac |
| institution | Directory Open Access Journal |
| issn | 1210-2709 1805-2363 |
| language | English |
| last_indexed | 2024-12-12T11:39:53Z |
| publishDate | 2004-01-01 |
| publisher | CTU Central Library |
| record_format | Article |
| series | Acta Polytechnica |
| spelling | doaj.art-194b111360c84b64a69fe0a7186a6eac2022-12-22T00:25:34ZengCTU Central LibraryActa Polytechnica1210-27091805-23632004-01-01445-6616Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint RuleP. KryslWe address the design of time integrators for mechanical systems that are explicit in the forcing evaluations. Our starting point is the midpoint rule, either in the classical form for the vector space setting, or in the Lie form for the rotation group. By introducing discrete, concentrated impulses we can approximate the forcing impressed upon the system over the time step, and thus arrive at first-order integrators. These can then be composed to yield a second order integrator with very desirable properties: symplecticity and momentum conservation.https://ojs.cvut.cz/ojs/index.php/ap/article/view/616Time integrationrigid body motionmidpoint rulesymplectic EulerVerletNewmarkmidpoint Lie algorithm |
| spellingShingle | P. Krysl Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule Acta Polytechnica Time integration rigid body motion midpoint rule symplectic Euler Verlet Newmark midpoint Lie algorithm |
| title | Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule |
| title_full | Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule |
| title_fullStr | Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule |
| title_full_unstemmed | Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule |
| title_short | Explicit Time Integrators for Nonlinear Dynamics Derived from the Midpoint Rule |
| title_sort | explicit time integrators for nonlinear dynamics derived from the midpoint rule |
| topic | Time integration rigid body motion midpoint rule symplectic Euler Verlet Newmark midpoint Lie algorithm |
| url | https://ojs.cvut.cz/ojs/index.php/ap/article/view/616 |
| work_keys_str_mv | AT pkrysl explicittimeintegratorsfornonlineardynamicsderivedfromthemidpointrule |