Quasi-canonicalization for linear homogeneous nonholonomic systems

doi:10.1088/1674-1056/ab8627

Abstract For conservative linear homogeneous nonholonomic systems, there exists a cotangent bundle with the symplectic structure dπ^μ∧dξ_μ, in which the motion equations of the system can be written into the form of the canonical equations by the set of quasi-coordinates π^μ and quasi-momenta ξ_μ. The key to construct this cotangent bundle is to define a set of suitable quasi-coordinates π^μ 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.

Keywords: quasi-canonicalization nonholonomic systems first-order linear mapping Hamilton-Jacobi method

Received: 08 February 2020
Revised: 13 March 2020
Accepted manuscript online:

PACS:	45.20.Jj	(Lagrangian and Hamiltonian mechanics)
	02.40.Yy	(Geometric mechanics)
	45.50.-j	(Dynamics and kinematics of a particle and a system of particles)
	02.40.Ky	(Riemannian geometries)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11972177, 11972122, 11802103, 11772144, 11872030, and 11572034) and the Scientific Research Starting Foundation for Scholars with Doctoral Degree of Guangdong Medical University (Grant Nos. B2019042 and B2019021).

Corresponding Authors: Yong-Xin Guo
E-mail: yxguo@lnu.edu.cn

Cite this article:

Yong Wang(王勇), Jin-Chao Cui(崔金超), Ju Chen(陈菊), Yong-Xin Guo(郭永新) Quasi-canonicalization for linear homogeneous nonholonomic systems 2020 Chin. Phys. B 29 064501

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Quasi-canonicalization for linear homogeneous nonholonomic systems

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