LEADER 05822nam 2200733 a 450 001 9910780893703321 005 20230726183238.0 010 $a1-282-76167-6 010 $a9786612761676 010 $a981-4289-49-3 035 $a(CKB)2490000000001743 035 $a(EBL)1679291 035 $a(OCoLC)630164386 035 $a(SSID)ssj0000418549 035 $a(PQKBManifestationID)11299180 035 $a(PQKBTitleCode)TC0000418549 035 $a(PQKBWorkID)10370825 035 $a(PQKB)10440075 035 $a(MiAaPQ)EBC1679291 035 $a(WSP)00000685 035 $a(Au-PeEL)EBL1679291 035 $a(CaPaEBR)ebr10421983 035 $a(CaONFJC)MIL276167 035 $a(EXLCZ)992490000000001743 100 $a20090622d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGeometry of nonholonomically constrained systems$b[electronic resource] /$fRichard Cushman, Hans Duistermaat, Je?drzej S?niatycki 210 $aSingapore ;$aHackensack, NJ $cWorld Scientific$dc2010 215 $a1 online resource (421 p.) 225 1 $aAdvanced series in nonlinear dynamics ;$vv. 26 300 $aDescription based upon print version of record. 311 $a981-4289-48-5 320 $aIncludes bibliographical references (p. 387-393) and index. 327 $aContents; Acknowledgments; Foreword; 1. Nonholonomically constrained motions; 1.1 Newton's equations; 1.2 Constraints; 1.3 Lagrange-d'Alembert equations; 1.4 Lagrange derivative in a trivialization; 1.5 Hamilton-d'Alembert equations; 1.6 Distributional Hamiltonian formulation; 1.6.1 The symplectic distribution (H,); 1.6.2 H and in a trivialization; 1.6.3 Distributional Hamiltonian vector field; 1.7 Almost Poisson brackets; 1.7.1 Hamilton's equations; 1.7.2 Nonholonomic Dirac brackets; 1.8 Momenta and momentum equation; 1.8.1 Momentum functions; 1.8.2 Momentum equations 327 $a1.8.3 Homogeneous functions1.8.4 Momenta as coordinates; 1.9 Projection principle; 1.10 Accessible sets; 1.11 Constants of motion; 1.12 Notes; 2. Group actions and orbit spaces; 2.1 Group actions; 2.2 Orbit spaces; 2.3 Isotropy and orbit types; 2.3.1 Isotropy types; 2.3.2 Orbit types; 2.3.3 When the action is proper; 2.3.4 Stratification on by orbit types; 2.4 Smooth structure on an orbit space; 2.4.1 Differential structure; 2.4.2 The orbit space as a differential space; 2.5 Subcartesian spaces; 2.6 Stratification of the orbit space by orbit types; 2.6.1 Orbit types in an orbit space 327 $a2.6.2 Stratification of an orbit space2.6.3 Minimality of S; 2.7 Derivations and vector fields on a differential space; 2.8 Vector fields on a stratified differential space; 2.9 Vector fields on an orbit space; 2.10 Tangent objects to an orbit space; 2.10.1 Stratified tangent bundle; 2.10.2 Zariski tangent bundle; 2.10.3 Tangent cone; 2.10.4 Tangent wedge; 2.11 Notes; 3. Symmetry and reductio; 3.1 Dynamical systems with symmetry; 3.1.1 Invariant vector fields; 3.1.2 Reduction of symmetry; 3.1.3 Reduction for or a free and proper G-action; 3.1.4 Reduction of a nonfree, proper G-action 327 $a3.2 Nonholonomic singular reduction for a proper action3.3 Nonholonomic reduction for a free and proper action; 3.4 Chaplygin systems; 3.5 Orbit types and reduction; 3.6 Conservation laws; 3.6.1 Momentum map; 3.6.2 Gauge momenta; 3.7 Lifted actions and the momentum equation; 3.7.1 Lifted actions; 3.7.2 Momentum equation; 3.8 Notes; 4.Reconstruction, relative equilibria and relative periodic orbits; 4.1 Reconstruction; 4.1.1 Reconstruction for proper free actions; 4.1.2 Reconstruction for nonfree proper actions; 4.1.3 Application to nonholonomic systems; 4.2 Relative equilibria 327 $a4.2.1 Basic properties4.2.2 Quasiperiodic relative equilibria; 4.2.3 Runaway relative equilibria; 4.2.4 Relative equilibria when the action is not free; 4.2.5 Other relative equilibria in a G-orbit; 4.2.5.1 When the G-action is free; 4.2.5.2 When the G-action is not free; 4.2.6 Smooth families of quasiperiodic relative equilibria; 4.2.6.1 Elliptic, regular, and stably elliptic elements of g; 4.2.6.2 When the G-action is free and proper; 4.2.6.3 When the G-action is proper but not free; 4.3 Relative periodic orbits; 4.3.1 Basic properties; 4.3.2 Quasiperiodic relative periodic orbits 327 $a4.3.3 Runaway relative period orbits 330 $aThis book gives a modern differential geometric treatment of linearly nonholonomically constrained systems. It discusses in detail what is meant by symmetry of such a system and gives a general theory of how to reduce such a symmetry using the concept of a differential space and the almost Poisson bracket structure of its algebra of smooth functions. The above theory is applied to the concrete example of Carathe?odory's sleigh and the convex rolling rigid body. The qualitative behavior of the motion of the rolling disk is treated exhaustively and in detail. In particular, it classifies all mot 410 0$aAdvanced series in nonlinear dynamics ;$vv. 26. 606 $aNonholonomic dynamical systems 606 $aGeometry, Differential 606 $aRigidity (Geometry) 606 $aCaratheodory measure 615 0$aNonholonomic dynamical systems. 615 0$aGeometry, Differential. 615 0$aRigidity (Geometry) 615 0$aCaratheodory measure. 676 $a516.3/6 700 $aCushman$b Richard H.$f1942-$044131 701 $aDuistermaat$b J. J$g(Johannes Jisse),$f1942-2010.$01370979 701 $aS?niatycki$b Je?drzej$040466 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910780893703321 996 $aGeometry of nonholonomically constrained systems$93787695 997 $aUNINA