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`PartialCompliantWithRelativeStates`

Defines relative angular states for compliant rotational connections.

This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:

\[\begin{align*} \frac{d\phi_{rel}}{dt} = w_{rel}\\ \frac{dw_{rel}}{dt} = a_{rel} \end{align*}\]

where $\phi_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.

This component extends from PartialCompliant

Usage

RotationalComponents.PartialCompliantWithRelativeStates()

Connectors

spline_a - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)
spline_b - This connector represents a rotational spline with angle and torque as the potential and flow variables, respectively. (Spline)

Variables

Name	Description	Units
`phi_rel`	Relative rotation angle between splineb and splinea	rad
`tau`	Torque transmitted between the splines	N.m
`w_rel`	Relative angular velocity between splines	rad/s
`a_rel`	Relative angular acceleration between splines	rad/s2

Source

"""
Defines relative angular states for compliant rotational connections.

This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:math \begin{align} \frac{d\phi{rel}}{dt} = w{rel}\
\frac{dw{rel}}{dt} = a{rel} \end{align}
where $\phi_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.
"""</span>
<span class="hljs-keyword">partial</span> <span class="hljs-keyword">component</span> PartialCompliantWithRelativeStates
&nbsp;&nbsp;<span class="hljs-keyword">extends</span> <span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/RotationalComponents/types/PartialCompliant.html">PartialCompliant</a></span>
&nbsp;&nbsp;<span class="hljs-comment">"Relative angular velocity between splines"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">w_rel</span>::<span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/Dyad/types/AngularVelocity.html">AngularVelocity</a></span>
&nbsp;&nbsp;<span class="hljs-comment">"Relative angular acceleration between splines"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">a_rel</span>::<span class="hljs-link"><a href="https://help.juliahub.com/dyad/dev/stdlib/Dyad/types/AngularAcceleration.html">AngularAcceleration</a></span>
<span class="hljs-keyword">relations</span>
&nbsp;&nbsp;der(phi_rel) = w_rel
&nbsp;&nbsp;der(w_rel) = a_rel
<span class="hljs-keyword">end</span></code></pre>

Flattened Source
"""
Defines relative angular states for compliant rotational connections.

This partial component extends a base compliant model by explicitly defining the relative angular velocity ($w_{rel}$) and relative angular acceleration ($a_{rel}$) between two connected rotational elements. These variables are intended to be used as preferred state variables. The core dynamics are described by the differential equations:math \begin{align} \frac{d\phi{rel}}{dt} = w{rel}\
\frac{dw{rel}}{dt} = a{rel} \end{align}
where $\phi_{rel}$ (relative angle) is assumed to be defined in the extended or extending components. This formulation is common in mechanical systems where relative motion is of primary interest.
"""</span>
<span class="hljs-keyword">partial</span> <span class="hljs-keyword">component</span> PartialCompliantWithRelativeStates
&nbsp;&nbsp;<span class="hljs-comment">"First rotational spline interface"</span>
&nbsp;&nbsp;<span class="hljs-symbol">spline_a</span> = <span>Spline</span>() {"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}
&nbsp;&nbsp;<span class="hljs-comment">"Second rotational spline interface"</span>
&nbsp;&nbsp;<span class="hljs-symbol">spline_b</span> = <span>Spline</span>() {"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}
&nbsp;&nbsp;<span class="hljs-comment">"Relative rotation angle between spline_b and spline_a"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">phi_rel</span>::<span>Angle</span>
&nbsp;&nbsp;<span class="hljs-comment">"Torque transmitted between the splines"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">tau</span>::<span>Torque</span>
&nbsp;&nbsp;<span class="hljs-comment">"Relative angular velocity between splines"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">w_rel</span>::<span>AngularVelocity</span>
&nbsp;&nbsp;<span class="hljs-comment">"Relative angular acceleration between splines"</span>
&nbsp;&nbsp;<span class="hljs-keyword">variable</span> <span class="hljs-symbol">a_rel</span>::<span>AngularAcceleration</span>
<span class="hljs-keyword">relations</span>
&nbsp;&nbsp;phi_rel = spline_b.phi - spline_a.phi
&nbsp;&nbsp;spline_b.tau = tau
&nbsp;&nbsp;spline_a.tau = -tau
&nbsp;&nbsp;der(phi_rel) = w_rel
&nbsp;&nbsp;der(w_rel) = a_rel
<span class="hljs-keyword">metadata</span> {}
<span class="hljs-keyword">end</span></code></pre>




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