The two-dimensional nonlinear system is described by x=-y(y²-b²) y = x(x²-b²) i-Find and classify the equilibrium point(s), where b is a positive constant. ii-Does the system is conservative? Confirm the answer.

The two-dimensional nonlinear system is described by x=-y(y²-b²) y = x(x²-b²) i-Find and classify the equilibrium point(s), where b is a positive constant. ii-Does the system is conservative? Confirm the answer.

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter10: Virtual Work And Potential Energy

Section: Chapter Questions

Problem 10.57P: Find the stable equilibrium position of the system described in Prob. 10.56 if m = 2.06 kg.

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Chemical and Phase Equilibrium

Phase diagrams or equilibrium phase diagrams are the graphical representations that show the phase transformations of the constituting elements with respect to the pressure, temperature, and compositions. The diagrams show the conditions that limit the different phases, namely solid, liquid, and gas. The diagram can also be utilized to verify the relations between the state variables. Most of the phase diagrams are temperature-pressure phase diagrams, with the variable parameter as the composition. Usually other variables such as solubility and pressure parameters are not indicated in the phase diagram. For a one-component system (unary phase diagram), the phase diagram is generally a function of temperature and pressure as the state variables, or temperature and volume. However, for a binary system (two-phase) having two components, the phase diagram is a function of temperature and composition as the state variables only. Coexisting of the different phases of the constituting elements is indicated in the phase diagram. A ternary phase diagram can be characterized by consisting of three phases in equilibrium.

Question

The two-dimensional nonlinear system is described by
x = -y(y²-b²)
y = x(x² - 6²)
i-Find and classify the equilibrium point(s), where b is a positive constant.
ii-Does the system is conservative? Confirm the answer.

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