Conformal invariance and conserved quantity of Mei symmetry for Appell equations in nonholonomic systems of Chetaev’s type with variable mass

Fang, Zhang; Li, Wei; Zhang, Yaoyu; Xi-chang, Xue; Li-Qun, Jia

doi:10.7498/aps.63.164501

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…The linear differential constrained system [1][2][3] is an important research object of analytical mechanics. [4][5][6][7][8][9][10][11] And linear differential constraints exist widely in many engineering problems, such as robots, bicycles, skateboards, electromechanical coupling systems, and so on. Many of these linear differential constraints are homogeneous.…”

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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