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| A parameter-preadjusted symplectic algorithm for planar rigid body systems |
| Received:August 26, 2023 Revised:October 17, 2023 |
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| DOI：10.7511/jslx20230826001 |
| KeyWord:planar rigid body systems Cartesian coordinates orthogonal projection symplectic algorithm high-precision |
| Author | Institution |
| 吴志刚 |
中山大学·深圳 航空航天学院, 深圳 |
| 徐小明 |
中山大学·深圳 航空航天学院, 深圳 |
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| Abstract: |
| Symplectic integrations have important applications for constrained Hamiltonian systems because they exhibit excellent stability in long-time simulations.However, the symplectic scheme usually has a large phase error accumulation with the increase of simulation time.This paper develops a parameter-preadjusted symplectic integration for planar rigid multibody systems with Cartesian coordinates.By deriving the modified Lagrangian equation with undetermined parameters, combining it with the existing symplectic scheme, and adjusting the corresponding parameter in advance, the symplectic method can greatly reduce the phase error of the numerical solution.Theoretical analysis and numerical results show that the new method not only preserves the symplectic structure of the flow but also presents a very low phase error accumulation.Therefore, the parameter-preadjusted symplectic integration is recommended for long-time simulations. |