Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators

SHEN Shilei; SONG Chuanjing

doi:10.21656/1000-0887.430091

Volume 43 Issue 12

Dec. 2022

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SHEN Shilei, SONG Chuanjing. Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1422-1433. doi: 10.21656/1000-0887.430091

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Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators

doi: 10.21656/1000-0887.430091

SHEN Shilei,
SONG Chuanjing^,

School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou, Jiangsu 215009, P.R.China

Received Date: 2022-03-21
Rev Recd Date: 2022-04-14

Available Online: 2022-12-20

Publish Date: 2022-12-01

Abstract

Abstract

Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results.
- generalized operator,
- singular system,
- primary constraint,
- constrained Hamilton equation,
- Noether’s theorem,
- symmetry and conserved quantity

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References(33)

References

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