Ratings
=========


+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|SLF                                      |Friction Limit Surface                                                                                        |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{M}_{y}`                          |Moment in the assembly around the :math:`y` axis                                                              |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{N}}_{1}`               |Maximum sliding force of the assembly on the :math:`x` axis                                                   |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{M}}_{1}`               |Slip moment limit of the assembly on the axis :math:`y`                                                       |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|SLU                                      |Ultimate Boundary Area                                                                                        |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{N}}_{2}`               |Ultimate assembly effort on the :math:`x` axis                                                                |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{M}}_{2}`               |Ultimate assembly moment on the :math:`y` axis                                                                |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\overline{N}`                     |Limit effort                                                                                                  |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\overline{M}`                     |Boundary moment                                                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{U}}_{1}`               |Limited displacement of mechanism 1 on the :math:`x` axis                                                     |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{\mathrm{\theta }}}_{1}`|Limited rotation of mechanism 1 on the :math:`y` axis                                                         |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{U}}_{2}`               |Limited displacement of mechanism 2 on the :math:`x` axis                                                     |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\overline{\mathrm{\theta }}}_{2}`|Limited rotation of mechanism 2 on the :math:`y` axis                                                         |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`U`                                |Moving the assembly on the :math:`x` axis                                                                     |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\mathrm{\theta }`                 |Rotation of the assembly on the :math:`y` axis                                                                |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`n`                                |Reduced effort :math:`n=\text{Nx}/\overline{N}`                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`m`                                |Reduced moment :math:`m=\text{My}/\overline{M}`                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{U}_{r}`                          |Reduced displacement :math:`\text{Ur}=U/\overline{U}`                                                         |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{\mathrm{\theta }}_{r}`           |Reduced rotation :math:`\mathrm{\theta }r=\mathrm{\theta }/\overline{\mathrm{\theta }}`                       |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\overline{U}`                     |Limit displacement on the :math:`x` axis                                                                      |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\overline{\mathrm{\theta }}`      |Rotation limit on the :math:`y` axis                                                                          |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`h(x)`                             |Scalar function                                                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`a`                                |Nonlinearity parameter                                                                                        |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\overline{d}`                     |Scalar constant                                                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\underline{d}`                    |Reduced generalized displacement vector                                                                       |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\underline{f}`                    |Reduced generalized effort vector                                                                             |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`p`                                |Scalar internal variable                                                                                      |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\text{feq}`                       |Scalar reduced equivalent generalized effort                                                                  |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`F`                                |Loading area                                                                                                  |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`R(x)`                             |Scalar function :math:`R(x)={h}^{-1}(x)`                                                                      |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\underline{D}`                    |Generalized displacement vector                                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\underline{F}`                    |Generalized effort vector                                                                                     |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\left[\overline{D}\right]`        |Generalized displacement limit matrix                                                                         |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\left[\overline{F}\right]`        |Generalized effort limit matrix                                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{X}^{\text{+}}`                   |Value of :math:`X` at time :math:`t+\mathit{dt}`                                                              |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{X}^{\text{-}}`                   |Value of :math:`X` at time :math:`t`                                                                          |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`e`                                |Charging eccentricity :math:`e={M}_{y}/{N}_{x}`                                                               |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{e}_{r}`                          |Reduced loading eccentricity :math:`{e}_{r}=m/n`                                                              |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\mathrm{\varepsilon }`            |Sign of                                                                                                       |
+                                         +                                                                                                              +
|                                         |                                                                                                              |
+                                         + .. image:: images/Object_50.svg                                                                              +
|                                         |    :width: 13                                                                                                |
+                                         +    :height: 14                                                                                               +
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+                                         +                                                                                                              +
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+                                         +                                                                                                              +
|                                         |                                                                                                              |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\left[\right]`                    |Matrix                                                                                                        |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\left\{\right\}`                  |Column vector                                                                                                 |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`\text{< >}`                       |Line vector                                                                                                   |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{K}_{o}`                          |Tangent operator at the moment :math:`t`                                                                      |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{K}_{n}`                          |Tangent operator at the moment :math:`t+\mathrm{dt}`                                                          |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+
|:math:`{K}_{\text{or}},{K}_{\text{nr}}`  |Reduced tangent operators                                                                                     |
+-----------------------------------------+--------------------------------------------------------------------------------------------------------------+