PartialCompliantWithRelativeStates
IconPartialCompliantWithRelativeStates
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.
Usage
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.
partial component PartialCompliantWithRelativeStates
extends PartialCompliant
# Relative angular velocity between splines
variable w_rel::AngularVelocity
# Relative angular acceleration between splines
variable a_rel::AngularAcceleration
relations
der(phi_rel) = w_rel
der(w_rel) = a_rel
end
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.
partial component PartialCompliantWithRelativeStates
# First rotational spline interface
spline_a = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
# Second rotational spline interface
spline_b = Spline() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
# Relative rotation angle between spline_b and spline_a
variable phi_rel::Angle
# Torque transmitted between the splines
variable tau::Torque
# Relative angular velocity between splines
variable w_rel::AngularVelocity
# Relative angular acceleration between splines
variable a_rel::AngularAcceleration
relations
phi_rel = spline_b.phi-spline_a.phi
spline_b.tau = tau
spline_a.tau = -tau
der(phi_rel) = w_rel
der(w_rel) = a_rel
metadata {}
end
Test Cases
No test cases defined.
Related
- Examples
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