# LR and L+R systems

@article{Jovanovic2009LRAL, title={LR and L+R systems}, author={B. Jovanovic}, journal={Journal of Physics A}, year={2009}, volume={42}, pages={225202} }

We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study n-dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrization becomes an integrable Hamiltonian system on the (n − 1)-dimensional sphere. Also, we showed that an arbitrary L+R system introduced by Fedorov can be seen as a reduced system of… Expand

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Invariant measures of modified LR and L+R systems

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We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: LR and L+R systems. As an example, we study a modified Veselova… Expand

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We study a time reparametrisation of the Newton type equations on Riemannian manifolds slightly modifying the Chaplygin multiplier method, allowing us to consider the Chaplygin method and the… Expand

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We consider nonholonomic Chaplygin systems and associate to them a $(1,2)$ tensor field on the shape space, that we term the gyroscopic tensor, and that measures the interplay between the… Expand

Hamiltonization and Integrability of the Chaplygin Sphere in ℝn

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- J. Nonlinear Sci.
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It is proved that for a specific choice of the inertia operator, the restriction of the generalized problem onto a zero value of the SO(n−1)-momentum mapping becomes an integrable Hamiltonian system after an appropriate time reparametrization. Expand

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We study the rolling of the Chaplygin ball and the rubber Chaplygin ball in $\mathbb R^n$ over a fixed $(n-1)$--dimensional sphere. The problems can be naturally considered within a framework of… Expand

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The reduced equations of motion in terms of the mass tensor of the body are derived and it is shown that in some previously known instances of integrability, the flow is quasiperiodic without the need of a time reparametrization. Expand

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