Matches in SemOpenAlex for { <https://semopenalex.org/work/W4301630103> ?p ?o ?g. }
Showing items 1 to 61 of
61
with 100 items per page.
- W4301630103 abstract "A nonholonomic system consists of a configuration space Q, a Lagrangian L, and an nonintegrable constraint distribution H, with dynamics governed by Lagrange-d'Alembert's principle. We present two studies both using adapted moving frames. In the first study we apply Cartan's method of equivalence to investigate the geometry underlying a nonholonomic system. As an example we compute the differential invariants for a nonholonomic system on a four-dimensional configuration manifold endowed with a rank two (Engel) distribution. In the second part we study G-Chaplygin systems. These are systems where the constraint distribution is given by a connection on a principal fiber bundle with total space Q and base space S=Q/G, and with a G-equivariant Lagrangian. These systems compress to an almost Hamiltonian system on $T^{*}S$. Under an $s in S$ dependent time reparameterization a number of compressed systems become Hamiltonian. A necessary condition for Hamiltonization is the existence of an invariant measure on the original system. Assuming an invariant measure we describe the obstruction to Hamiltonization. Chaplygin's rubber sphere, a ball with unequal inertia coefficients rolling without slipping or spinning (about the vertical axis) on a plane is Hamiltonizable when compressed to $T^{*}SO(3)$. Finally we discuss reduction of internal symmetries. Chaplygin's marble (where spinning is allowed) is not Hamiltonizable when compressed to $T^{*}SO(3)$; we conjecture that it is also not Hamiltonizable when reduced to $T^{*}S^{2}$." @default.
- W4301630103 created "2022-10-05" @default.
- W4301630103 creator A5003809086 @default.
- W4301630103 creator A5007725876 @default.
- W4301630103 creator A5049933893 @default.
- W4301630103 creator A5067012800 @default.
- W4301630103 date "2004-08-02" @default.
- W4301630103 modified "2023-10-18" @default.
- W4301630103 title "Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization" @default.
- W4301630103 doi "https://doi.org/10.48550/arxiv.math-ph/0408005" @default.
- W4301630103 hasPublicationYear "2004" @default.
- W4301630103 type Work @default.
- W4301630103 citedByCount "0" @default.
- W4301630103 crossrefType "posted-content" @default.
- W4301630103 hasAuthorship W4301630103A5003809086 @default.
- W4301630103 hasAuthorship W4301630103A5007725876 @default.
- W4301630103 hasAuthorship W4301630103A5049933893 @default.
- W4301630103 hasAuthorship W4301630103A5067012800 @default.
- W4301630103 hasBestOaLocation W43016301031 @default.
- W4301630103 hasConcept C121332964 @default.
- W4301630103 hasConcept C121770821 @default.
- W4301630103 hasConcept C134306372 @default.
- W4301630103 hasConcept C138632511 @default.
- W4301630103 hasConcept C151300846 @default.
- W4301630103 hasConcept C154945302 @default.
- W4301630103 hasConcept C19966478 @default.
- W4301630103 hasConcept C33923547 @default.
- W4301630103 hasConcept C41008148 @default.
- W4301630103 hasConcept C62520636 @default.
- W4301630103 hasConcept C74650414 @default.
- W4301630103 hasConcept C90509273 @default.
- W4301630103 hasConcept C90738871 @default.
- W4301630103 hasConceptScore W4301630103C121332964 @default.
- W4301630103 hasConceptScore W4301630103C121770821 @default.
- W4301630103 hasConceptScore W4301630103C134306372 @default.
- W4301630103 hasConceptScore W4301630103C138632511 @default.
- W4301630103 hasConceptScore W4301630103C151300846 @default.
- W4301630103 hasConceptScore W4301630103C154945302 @default.
- W4301630103 hasConceptScore W4301630103C19966478 @default.
- W4301630103 hasConceptScore W4301630103C33923547 @default.
- W4301630103 hasConceptScore W4301630103C41008148 @default.
- W4301630103 hasConceptScore W4301630103C62520636 @default.
- W4301630103 hasConceptScore W4301630103C74650414 @default.
- W4301630103 hasConceptScore W4301630103C90509273 @default.
- W4301630103 hasConceptScore W4301630103C90738871 @default.
- W4301630103 hasLocation W43016301031 @default.
- W4301630103 hasOpenAccess W4301630103 @default.
- W4301630103 hasPrimaryLocation W43016301031 @default.
- W4301630103 hasRelatedWork W1997865612 @default.
- W4301630103 hasRelatedWork W201620459 @default.
- W4301630103 hasRelatedWork W2056993080 @default.
- W4301630103 hasRelatedWork W2079337912 @default.
- W4301630103 hasRelatedWork W2131752647 @default.
- W4301630103 hasRelatedWork W2134149732 @default.
- W4301630103 hasRelatedWork W2263019585 @default.
- W4301630103 hasRelatedWork W3049762938 @default.
- W4301630103 hasRelatedWork W4284968746 @default.
- W4301630103 hasRelatedWork W572944523 @default.
- W4301630103 isParatext "false" @default.
- W4301630103 isRetracted "false" @default.
- W4301630103 workType "article" @default.