LEADER 04976nam 22006374a 450 001 9910784984803321 005 20230607221557.0 010 $a981-277-807-1 035 $a(CKB)1000000000408471 035 $a(EBL)1681534 035 $a(OCoLC)879074416 035 $a(SSID)ssj0000129793 035 $a(PQKBManifestationID)11139114 035 $a(PQKBTitleCode)TC0000129793 035 $a(PQKBWorkID)10078942 035 $a(PQKB)11601836 035 $a(MiAaPQ)EBC1681534 035 $a(WSP)00004879 035 $a(Au-PeEL)EBL1681534 035 $a(CaPaEBR)ebr10201240 035 $a(CaONFJC)MIL505434 035 $a(EXLCZ)991000000000408471 100 $a20020514d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aContemporary trends in nonlinear geometric control theory and its applications$b[electronic resource] /$fA. Anzaldo-Meneses ... [et al.] 210 $aRiver Edge, NJ $cWorld Scientific$dc2002 215 $a1 online resource (496 p.) 300 $aDescription based upon print version of record. 311 $a981-02-4841-5 320 $aIncludes bibliographical references and index. 327 $aContents ; Foreword ; Part I Invited Survey Chapters ; Variational Problems on Lie Groups and their Homogeneous Spaces: Elastic Curves Tops and Constrained Geodesic Problems ; 1. Introduction ; 2. Space forms and their frame bundles ; 3. Hamiltonians and the extremal curves 327 $aControllability of Lie Systems 1. Introduction ; 2. Control systems on Lie groups ; 3. Groups irrelevant for transitivity ; 4. Exploiting compactness and irrelevancy ; 5. Irrelevant groups and algebras ; 6. Irrelevant groups and algebras: the solvable case 327 $a7. Irrelevant groups and algebras: the semisimple case Canonical Contact Systems for Curves: A Survey ; 1. Introduction ; 2. The canonical contact system for curves ; 3. History ; 4. Involutive subdistributions of corank one 327 $a5. Contact systems characteristic distributions and involutive subdistributions 6. Flatness of contact systems ; 7. An example ; 8. Singular points and extended Kumpera-Ruiz normal forms ; The Brachistochrone Problem and Modern Control Theory ; 1. Introduction 327 $a2. Johann Bernoulli and the brachistochrone problem 3. The standard formulation and Johann Bernoulli's solution ; 4. Spurious solutions and the calculus of variations approach ; 5. The optimal control approach ; 6. The differential-geometric connection 327 $a7. Five modern variations on the theme of the brachistochrone 330 $a Mathematical control theory has evolved from the study of practical problems in engineering and sciences to the elaboration of deep, important concepts in mathematics and applied sciences. This volume concerns contemporary trends in nonlinear geometric control theory and its applications. It is a fine collection of papers presenting new results, relevant open problems, and important applications regarding academic and real-world problems. The book is dedicated to Velimir Jurdjevic whose scientific activity has been influential in the research of many of the authors. It contains a number of a 606 $aNonlinear control theory 606 $aGeometry, Differential 606 $aExterior differential systems 615 0$aNonlinear control theory. 615 0$aGeometry, Differential. 615 0$aExterior differential systems. 676 $a629.8/312 701 $aAnzaldo-Meneses$b A$01499524 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910784984803321 996 $aContemporary trends in nonlinear geometric control theory and its applications$93725623 997 $aUNINA