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| Approximate conservation laws for dynamic systems with symmetry breaking in symplectic framework |
| Received:August 31, 2023 Revised:November 01, 2023 |
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| DOI：10.7511/jslx20230831001 |
| KeyWord:approximate conservation law non-conservative symmetry breaking symplectic |
| Author | Institution |
| 胡伟鹏 |
西安理工大学 土木建筑工程学院, 西安 |
| 林志华 |
香港城市大学 建筑学及土木工程学系, 香港 |
| 邓子辰 |
西北工业大学 力学与土木建筑学院, 西安 |
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| Abstract: |
| Since the establishment of the symplectic geometric method for Hamiltonian systems by K.Feng, a globally recognized, prominent mathematician and scientist, the conservation laws including symplectic structures and energy conservation have become one of the effective verification criteria for numerical approaches of dynamic systems.However, some intrinsic system characteristics including damping dissipation, external excitation and control, variable coefficients, etc., that cause symmetry breaking in practical dynamic systems affect the system symmetry and conservation laws.In this paper, the approximate conservation laws of dynamic systems considering various symmetry breaking factors are analyzed in detail.Based on the geometric symmetry theory, the symplectic structure for finite-dimensional stochastic dynamic systems is obtained.Further, for infinite-dimensional non-conservative dynamic systems with various coefficients, time-space dependent Hamilton functions, and stochastic dynamic systems, the effects of symmetry breaking factors on local energy dissipation are investigated.The result established here may form the mathematical basis for symplectic analysis of dynamic systems with broken symmetry. |
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