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2011•Chinese Physics BOpen access

The approximate conserved quantity of the weakly nonholonomic mechanical-electrical system

刘晓巍, 李元成, Li-Li Xia

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Abstract

We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.

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We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.

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Available abstract

We study the approximate conserved quantity of the weakly nonholonomic mechanical-electrical system. By means of the Lagrange—Maxwell equation, the Noether equality of the weakly nonholonomic mechanical-electrical system is obtained. The multiple powers-series expansion of the parameter of the generators of infinitesimal transformations and the gauge function is put into a generalized Noether identity. Using the Noether theorem, we obtain an approximate conserved quantity. An example is provided to prove the existence of the approximate conserved quantity.

Key concepts: Noether's theorem, Nonholonomic system, Conserved quantity, Infinitesimal, Conserved current, Function (biology), Mathematical physics, Gauge (firearms)

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