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(b) The Lagrangian function of a mechanical system with one degree of freedom is ma – U(z), L = where U(x) = a(x* – 4x²) and m, a are positive constants. Find the equilibria and determine their linear stability. %3D

(b) The Lagrangian function of a mechanical system with one degree of freedom is ma – U(z), L = where U(x) = a(x* – 4x²) and m, a are positive constants. Find the equilibria and determine their linear stability. %3D

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(b) The Lagrangian function of a mechanical system with one degree of freedom is 1 L mi² – U (x), where U (x) = a(x4 – 4x²) and m, a are positive constants. Find the equilibria and determine their linear stability. -
Transcribed Image Text:(b) The Lagrangian function of a mechanical system with one degree of freedom is 1 L mi² – U (x), where U (x) = a(x4 – 4x²) and m, a are positive constants. Find the equilibria and determine their linear stability. -
(c) Draw the phase portrait of the system for m = a = 1 on the plane (x, à). Be precise about the direction of motion.
Transcribed Image Text:(c) Draw the phase portrait of the system for m = a = 1 on the plane (x, à). Be precise about the direction of motion.
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