Noether Symmetry of Automotive Electromagnetic Suspension Systems and Its Application
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摘要: 研究了含有电磁悬架汽车振动系统的Noether对称性,给出了系统的守恒量,并通过守恒量求得系统的对称性解.以能量形式,建立汽车不同振动形式下的Lagrange(拉格朗日)方程.选取位移坐标为广义坐标,研究了各种振动形式下系统的Noether对称性,并给出相应的Noether恒等式、Killing方程和广义Noether定理.研究系统守恒量,运用存在的守恒量,给出一种新的求解汽车振动系统响应的方法;并应用到具体的车体振动系统计算中,给出了系统在转弯、制动或加速等情况下的位移响应和速度响应曲线.
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关键词:
- 电磁悬架 /
- Lagrange方程 /
- Noether对称性 /
- 守恒量
Abstract: The Noether symmetry of vehicle vibration systems with electromagnetic suspension was studied, and the conserved quantity of the system was given. Furthermore, with the conserved quantity, the symmetry solution of the system was obtained. In the form of energy, the Lagrangian equations under different vibration modes were built. With the chosen displacement coordinates as the generalized coordinates, the Noether symmetries of the system under different vibration modes were studied, the corresponding Noether identities, Killing equations and generalized Noether theorems were given. The conserved quantity of the system was applied so that a new method for solving vehicle vibration system responses was proposed. Then this method was used in the calculation of a specific vehicle vibration system, and the displacement response curves and velocity response curves of the system in the cases of swerving, braking, accelerating and so on can be obtained. The calculation results agree well with the empirical data.-
Key words:
- electromagnetic suspension /
- Lagrangian equation /
- Noether symmetry /
- conserved quantity
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