Cds202-hw9_wi09

Cds202-hw9_wi09 - 4 MTA 8.2-1 pullback and exterior...

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CALIFORNIA INSTITUTE OF TECHNOLOGY Control and Dynamical Systems CDS 202 R. Murray Winter 2009 Problem Set #9 Issued: 5 Mar 09 Due: 12 Mar 09 Reading: Abraham, Marsden, and Ratiu (MTA), Sections 7.4–7.5, 8.1–8.2 Problems: 1. Calculate exterior derivatives of the following forms in R 3 : (a) z 2 dx dy + ( z 2 + 2 y ) dx dz (b) z 2 dx dy + ( z 2 + 2 y ) dx dz (c) f d g , where f and g are functions on R 3 (d) ( x + 2 y 3 )( dz dx + 1 2 dy dx ) 2. MTA, 7.4-3: practice with exterior derivatives 3. MTA, 7.5-6: divergence of a Lie bracket
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Unformatted text preview: 4. MTA, 8.2-1: pullback and exterior derivatives 5. MTA, 8.2-2: exterior derivative on a manifold without boundary 6. Consider the locomotion system given by a disk rolling on the plane from homework #7. Using the exterior derivative of the kinematic connection, determine if the system is totally controllable and/or fiber controllable....
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