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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1994 • Question 3

Question

Math 6410 • ODE Fall 1994 • Question 3

Let \(P\) and \(Q\) be infinitely differentiable. Prove that \(x'=P(x,y)\), \(y'=Q(x,y)\) is a Hamiltonian system iff \(x'=Q(x,y)\), \(y'=-P(x,y)\) is a gradient system.

Raw LaTeX

Let \(P\) and \(Q\) be infinitely differentiable. Prove that
\(x'=P(x,y)\), \(y'=Q(x,y)\) is a Hamiltonian system iff \(x'=Q(x,y)\), \(y'=-P(x,y)\) is a
gradient system.

Topic Tags

Hamiltonian Systems, Damped Oscillators, and Pendulums