Quasi-momentum theorem in Riemann-Cartan space

Liu, Chang; Xiao, Jing; Wang, Yong; Feng-Xiang, Mei

doi:10.1007/s10483-018-2323-6

Cited by 3 publications

(1 citation statement)

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“…In this paper, by the first-order linear nonholonomic mapping theory, [40][41][42][43] we will give a method to realize the quasi-canonicalization of linear homogeneous nonholonomic systems. That is, by introducing a set of suitable quasicoordinates π µ and quasi-momenta ξ µ , the motion equations of conservative linear homogeneous nonholonomic systems can be written as…”

Section: Introductionmentioning

confidence: 99%

Quasi-canonicalization for linear homogeneous nonholonomic systems*

Wang

Jinchao

et al. 2020

Chinese Phys. B

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For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπμ ∧ dξμ , in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates πμ and quasi-momenta ξμ . The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates πμ by a first-order linear mapping, so that the reduced configuration space of the system is a Riemann space with no torsion. The Hamilton–Jacobi method for linear homogeneous nonholonomic systems is studied as an application of the quasi-canonicalization. The Hamilton–Jacobi method can be applied not only to Chaplygin nonholonomic systems, but also to non-Chaplygin nonholonomic systems. Two examples are given to illustrate the effectiveness of the quasi-canonicalization and the Hamilton–Jacobi method.

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Section: Introductionmentioning

confidence: 99%