A Nonholonomic Model of the Paul Trap

Borisov, Alexey V.; Kilin, Alexander A.; Mamaev, Ivan S.

doi:10.1134/s1560354718030085

Cited by 7 publications

(1 citation statement)

References 24 publications

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“…Many of these linear differential constraints are homogeneous. [12][13][14][15][16][17][18][19][20][21][22][23][24] Linear differential constrained systems include holonomic systems and linear nonholonomic systems. When all differential constraints are integrable, the linear differential constrained system is called a holonomic system, and can be reduced into a geometric constrained system.…”

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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