力学系统的几何控制 英文

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1、FrancescoBulloandAndrewD.LewisGeometricControlofMechanicalSystemsModeling,Analysis,andDesignforSimpleMechanicalControlSystems–SupplementaryMaterial–February2,2005ContentsS1Tangentandcotangentbundlegeometry.................S1S1.1SomethingsHamiltonian...............................S1S1.1.1Di

2、fferentialforms...............................S1S1.1.2Symplecticmanifolds...........................S5S1.1.3Hamiltonianvectorfields........................S6S1.2Tangentandcotangentliftsofvectorfields...............S7S1.2.1Moreaboutthetangentlift......................S7S1.2.2Thecotangentliftof

3、avectorfield................S8S1.2.3Jointpropertiesofthetangentandcotangentlift...S9S1.2.4Thecotangentliftoftheverticallift..............S11S1.2.5ThecanonicalinvolutionofTTQ.................S12S1.2.6Thecanonicalendomorphismofthetangentbundle.S13S1.3Ehresmannconnectionsinducedbyanaffineconnect

4、ion....S13S1.3.1Motivatingremarks.............................S13S1.3.2Moreaboutvectorandfiberbundles..............S15S1.3.3Ehresmannconnections.........................S17S1.3.4Linearconnectionsandlinearvectorfieldsonvectorbundles.......................................S18S1.3.5TheEhresmannc

5、onnectiononπTM:TM→Massociatedwithasecond-ordervectorfieldonTM..S20S1.3.6TheEhresmannconnectiononπTQ:TQ→QassociatedwithanaffineconnectiononQ..........S21∗S1.3.7TheEhresmannconnectiononπT∗Q:TQ→QassociatedwithanaffineconnectiononQ..........S23S1.3.8TheEhresmannconnectiononπTTQ:TTQ→TQassociatedwith

6、anaffineconnectiononQ..........S23∗S1.3.9TheEhresmannconnectiononπT∗TQ:TTQ→TQassociatedwithanaffineconnectiononQ..........S25∗S1.3.10RepresentationsofSTandST...................S26S1.3.11TheSasakimetric..............................S33SiiContentsS2Controllability................................

7、...........S35S2.1Accessibilityandcontrollabilityofsystemswithabasicexternalforce.........................................S35S2.1.1Accessibilityresults.............................S36S2.1.2Controllabilityresults...........................S40S2.2Accessibilityof