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#: ../../source/behavior/functions/nonlinear.rst:4
msgid "Non-Linearities"
msgstr ""
"非线性"

#: ../../source/behavior/functions/nonlinear.rst:6
msgid ""
"Our next example involving functions demonstrates how to address issues that"
" come up when solving non-linear systems of equations that involve "
"functions."
msgstr ""
"下一个示例主要展示了如何解决非线性系统方程调用函数的问题。\ "

#: ../../source/behavior/functions/nonlinear.rst:10
msgid ""
"We'll start with a simple model that includes this simple mathematical "
"relationship:"
msgstr ""
"首先我们以一个简单的模型开始介绍。\ "
"该模型包含了非常简单的数学关系，如下所示："

#: ../../source/behavior/functions/nonlinear.rst:17
msgid ""
"where :math:`t` is time.  This model can be implemented in Modelica as "
"follows:"
msgstr ""
"其中，\ :math:`t`\ 表示时间。\ "
"上述模型在Modelica中的实现如下："

#: ../../source/behavior/functions/nonlinear.rst:23
msgid ""
"where the ``Quadratic`` function, which we will discuss shortly, evaluates a"
" quadratic polynomial."
msgstr ""
"其中，\ ``Quadratic``\ 函数用于二次多项式的计算。\ "
"我们在后面会对其进行简单的讨论。\ "

#: ../../source/behavior/functions/nonlinear.rst:26
msgid "Simulating this model gives the following solution for ``y``:"
msgstr ""
"对上述模型进行仿真，变量\ ``y``\ 的仿真结果如下图所示："

#: ../../source/behavior/functions/nonlinear.rst:31
msgid ""
"So far, all of this appears quite reasonable and, based on our previous "
"discussion on :ref:`polynomial-evaluation`, the implementation of "
"``Quadratic`` isn't likely to hold too many surprises.  However, let's make "
"things a little more complicated. Consider the following model:"
msgstr ""
"目前为止，所有的一切似乎都很合理。\ "
"基于前面章节\ :ref:`polynomial-evaluation`\ 中的讨论，\ ``Quadratic``\ 函数的使用似乎也在"
"意料之中。\ "
"但是，对于如下所示的更加复杂的模型："

#: ../../source/behavior/functions/nonlinear.rst:41
msgid "This model amounts to solving the following equation:"
msgstr ""
"上述模型相当于求解下列方程："

#: ../../source/behavior/functions/nonlinear.rst:47
msgid ""
"The important difference here is that the left hand side is known and we "
"must compute the value of :math:`y` that satisfies this equation. In other "
"words, instead of evaluating a quadratic polynomial, like we were doing in "
"the previous example, now we have to solve a quadratic equation."
msgstr ""
"明显的区别在于，上述模型中等式左边是已知的。\ "
"我们需要计算满足方程的\ :math:`y`\ 值。\ "
"换言之，不同于前面示例中计算二次多项式的值，"
"上述模型需对二次多项式进行求解。\ "

#: ../../source/behavior/functions/nonlinear.rst:53
msgid ""
"A model that requires solving a non-linear system of equations is not "
"remarkable by itself.  Modelica compilers are certainly more than capable of"
" recognizing and solving non-linear systems of equations (although these "
"methods usually depend on having a reasonable initial guess in order to "
"converge)."
msgstr ""
"需要求解非线性系统方程的模型并不太好。\ "
"Modelica编译器具有非凡识别和求解非线性系统方程的能力\ "
"（尽管为了收敛，这些方法通常需依赖于合理的初始猜测）。\ "

#: ../../source/behavior/functions/nonlinear.rst:59
msgid ""
"However, it turns out that in this case, **the Modelica compiler doesn't "
"actually need to solve a non-linear system**.  Although we couldn't know "
"this until we saw how the ``Quadratic`` function is implemented:"
msgstr ""
"但事实上，上述情况下\ **Modelica编译器并不需要求解一个非线性系统**\ 。\ "
"若我们了解了\ ``Quadratic``\ 函数是如何实现的，就能清楚的了解上述情况："

#: ../../source/behavior/functions/nonlinear.rst:69
msgid ""
"In particular, note the line specifying the ``inverse`` annotation. With "
"this function definition, we not only tell the Modelica compiler how to "
"evaluate the ``Quadratic`` function, but, through the ``inverse`` "
"annotation, we are also indicating that the ``InverseQuadratic`` function "
"should be used to compute ``x`` in terms of ``y``."
msgstr ""
"特别的，需重点注意上述代码中的\ ``inverse``\ 注释。\ "
"对于上述函数的定义，不仅告诉Modelica编译器如何求解\ ``Quadratic``\ 方程，而且"
"通过\ ``inverse``\ 注释利用\ ``InverseQuadratic``\ 函数可以计算得到变量\ ``x``\ 和变量\ ``y``\ 的关系。\ "

#: ../../source/behavior/functions/nonlinear.rst:76
msgid "The ``InverseQuadratic`` function is defined as follows:"
msgstr ""
"\ ``InverseQuadratic``\ 函数的定义如下所示："

#: ../../source/behavior/functions/nonlinear.rst:84
msgid ""
"Note that the ``InverseQuadratic`` function computes only the positive root "
"in the quadratic equation.  This can be both a good thing and a bad thing.  "
"By computing only a single root, we avoid the issue of having multiple "
"solutions when we invert the quadratic relationship.  However, if the "
"negative root happens to be the one you want, this can be a problem."
msgstr ""
"通过上述代码，可以看到\ ``InverseQuadratic``\ 函数只能计算二次方程的正根。\ "
"对我们来说，这个结果可好可坏。\ "
"只计算一个根的话，在转换二次函数关系时就可以避免多个解。\ "
"但是，如果你恰巧需要负根，就可能会产生相应的问题。\ "

#: ../../source/behavior/functions/nonlinear.rst:91
msgid ""
"In the case of our ``ImplicitEvaluation`` model, the Modelica compiler can "
"then substitute this inverse function into the equations.  So, where we "
"initially had, ignoring the coefficient arguments for the moment, the "
"following equation to solve:"
msgstr ""
"在上述\ ``ImplicitEvaluation``\ 模型中，Modelica编译器可以替代上述反函数方程。\ "
"因此，忽略当前方程的参数，需要求解的方程如下所示："

#: ../../source/behavior/functions/nonlinear.rst:100
msgid ""
"which must be solved as an implicit equation for :math:`y`, we can now solve"
" the following **explicit** equation:"
msgstr ""
"其中，必须求解变量\ :math:`y`\ 的隐式方程，可以得到如下所示\ **显式**\ 方程："

#: ../../source/behavior/functions/nonlinear.rst:107
msgid "by using the ``InverseQuadratic`` function as the inverse function."
msgstr ""
"而通过使用\ ``InverseQuadratic``\ 函数作为原函数的反函数。\ "

#: ../../source/behavior/functions/nonlinear.rst:109
msgid ""
"Simulating the ``ImplicitEvaluation`` model we get the following solution "
"for ``y``:"
msgstr ""
"对上述\ ``ImplicitEvaluation``\ 模型进行，可以得到变量\ ``y``\ 仿真结果，如下图所示："

#: ../../source/behavior/functions/nonlinear.rst:115
msgid ""
"Looking at this figure, we can see that, in fact, we got the correct result,"
" but, in general, without the need to solve the non-linear system that would"
" otherwise result from our ``ImplicitEvaluation`` model."
msgstr ""
"通过观察上图，可以发现，模型计算得到了正确的结果。\ "
"而且，一般情况下并不需要求解非线性系统。\ "
"否则，如果没有注解，那\ ``ImplicitEvaluation``\ 模型就会引入非线性的方程组。\ "
