| 汽车车体振动系统的对称性与守恒量研究 |
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| 引用本文： | 翟晓洋,傅景礼.汽车车体振动系统的对称性与守恒量研究[J].应用数学和力学,2015,36(12):1285-1293. |
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| 作者姓名： | 翟晓洋 傅景礼 |
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| 作者单位： | 浙江理工大学 数学物理研究所, 杭州 310018 |
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| 基金项目： | 国家自然科学基金（11272287；11472247） |
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| 摘 要： | 用Lie群方法研究汽车车体振动系统的对称性，寻找其存在的守恒量.以汽车车体做上下垂直振动和绕其质心的前后俯仰振动，采用Lagrange函数的方法，构建汽车车体振动系统.以此系统为对象，引入Lie群方法，给出该振动系统的Noether对称性理论与Lie对称性理论；由此推导该汽车系统存在的Noether对称性与Lie对称性，并得到系统相应的的守恒量.该方法对车体振动问题提出了新的对称性解法，同时扩大了Lie群方法的应用范围.
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| 关 键 词： | 汽车车体振动系统 Noether对称性 Lie对称性 守恒量 |
| 收稿时间： | 2015-05-07 |
Study on Symmetries and Conserved Quantities of Vehicle Body Vibration Systems |
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| Affiliation: | Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, P.R.China |
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| Abstract: | Symmetries and conserved quantities of vehicle body vibration systems were studied with the Lie group method. The vertical translational vibration and the pitching vibration around the mass center were addressed by means of the Lagrangian functions to construct the vehicle body vibration model. According to this vibration system, the Noether symmetry theory and the Lie symmetry theory were derived via the introduction of the Lie group method. The existence of the Noether symmetries and the Lie symmetries of the system were proved with the corresponding conserved quantities obtained. This work provides a new symmetry solution to the vehicle body vibration problem, and meanwhile expands the application scope of the Lie group method. |
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