Consider the linear system dY dt = a b c d Y. (a) For
Chapter , Problem 28(choose chapter or problem)
Consider the linear system dY dt = a b c d Y. (a) For which values of a, b, c, and d is the system Hamiltonian? Calculate the Hamiltonian function for these values. (b) For which values of a, b, c, and d is the system a gradient system? For these values, calculate a function whose gradient yields the system. (c) Can the linear system be Hamiltonian and a gradient system for identical values of a, b, c, and d? (d) Are there values of a, b, c, and d for which the linear system is neither Hamiltonian nor a gradient system?
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