Unformatted text preview: and φ . (a) Let Q = SE (2) × S 1 represent the con±guration space for the system. Compute the Lagrangian for the sytem and show that is invariant under the action of SE (2) given by translation and rotation as well as the subgroup of actions given just by translation. (b) Compute the kinematic connection for the system A : TQ → g corresponding to the system rolling without slipping. (c) Determine if the system is totally controllable and/or ±ber controllable. (d) (Optional) Construct an explicit trajectory that moves the system from an arbitrary initial con±guration q = ( x ,y ,θ ,φ ) to the origin....
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- Fall '08
- California Institute of Technology, R. Murray, semidirect product groups