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The simplest kind of an orbit is a fixed point, or an equilibrium. If a mechanical system is in a stable equilibrium state then a small push will result in a localized motion, for example, small oscillations as in the case of a pendulum. In a system with damping, a stable equilibrium state is moreover asymptotically stable. On the other hand ...
For example, if equilibrium is specified by a single chemical equation:, [24] ∑ j = 0 m ν j R j = 0 {\displaystyle \sum _{j=0}^{m}\nu _{j}R_{j}=0} where ν j is the stoichiometric coefficient for the j th molecule (negative for reactants, positive for products) and R j is the symbol for the j th molecule, a properly balanced equation will obey:
The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov . In simple terms, if the solutions that start out near an equilibrium point x e {\displaystyle x_{e}} stay near x e {\displaystyle x_{e}} forever, then x e {\displaystyle x_{e}} is ...
Le Chatelier–Braun principle analyzes the qualitative behaviour of a thermodynamic system when a particular one of its externally controlled state variables, say , changes by an amount , the 'driving change', causing a change , the 'response of prime interest', in its conjugate state variable , all other externally controlled state variables remaining constant.
Equilibrium constants are defined in terms of fugacity. If the gases are at sufficiently low pressure that they behave as ideal gases, the equilibrium constant can be defined as a quotient of partial pressures. An example of gas-phase equilibrium is provided by the Haber–Bosch process of ammonia synthesis.
It is useful when both parties are willing to cooperate in implementing the fair solution. Such solutions, particularly the Nash solution, were used to solve concrete economic problems, such as management–labor conflicts, on numerous occasions. [1] An alternative approach to bargaining is the positive approach. It studies how the surplus is ...
For a reversible reaction, the equilibrium constant can be measured at a variety of temperatures. This data can be plotted on a graph with ln K eq on the y -axis and 1 / T on the x axis. The data should have a linear relationship, the equation for which can be found by fitting the data using the linear form of the Van 't Hoff equation
Notes and Problems in Applied General Equilibrium Economics. North-Holland. ISBN 978-0-444-88449-7. ——, with Rimmer, Maureen T. (2002). Dynamic General Equilibrium Modelling for Forecasting and Policy: A Practical Guide and Documentation of MONASH. Contributions to economic analysis (256). Amsterdam: Elsevier. ISBN 0444512608.