consider the second order dynamical system for (q, p) R for which and p...

 

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consider the second order dynamical system for (q, p) € R² for which ȧ and p are given by Hamilton's equations for the function H=p² +9¹-9². Question 13(a): The system has M hyperbolic and N elliptic fixed points. Which of the following statements is true? OM+N=2 OM-N=2 OM+N = 3 O M - N = 1 OM+N=1 O None of the other options is true Question 13(b): There is a single elliptic fixed point in the region q≥ 0, p > 0. The period T of small oscillations around this elliptic fixed point is approximately OT~T OT~ √2T OT~ 2T OT 2√2T OT~√√2T O None of the other options is true Question 13(c): The phase portrait for the system has a separatrix. Which of the following points (q, p) is on the separatrix? O (0, 1) ○ (0, √2) O (1,0) O (√2,0 O (1,1) None of the other options is true consider the second order dynamical system for (q, p) € R² for which ȧ and p are given by Hamilton's equations for the function H=p² +9¹-9². Question 13(a): The system has M hyperbolic and N elliptic fixed points. Which of the following statements is true? OM+N=2 OM-N=2 OM+N = 3 O M - N = 1 OM+N=1 O None of the other options is true Question 13(b): There is a single elliptic fixed point in the region q≥ 0, p > 0. The period T of small oscillations around this elliptic fixed point is approximately OT~T OT~ √2T OT~ 2T OT 2√2T OT~√√2T O None of the other options is true Question 13(c): The phase portrait for the system has a separatrix. Which of the following points (q, p) is on the separatrix? O (0, 1) ○ (0, √2) O (1,0) O (√2,0 O (1,1) None of the other options is true

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sol Given vale Hamiltonian H p 92 2 4 2 13 0 The mathematical expression ... View the full answer