PrescribeInitialVelocity

Sets a defined initial angular velocity to a rotational mechanical connector.

This component is used to define and enforce a specific initial angular velocity (w_0) on a rotational mechanical system at the commencement of a simulation. It interfaces with the system through a spline, which acts as a rotational connector. The component ensures that at time t=0, the angular velocity w of the connector is precisely equal to the user-defined parameter w_0. The relationship $\frac{d\text{spline.phi}}{dt} = w$ establishes that w is indeed the angular velocity of the spline connector. Importantly, the torque transmitted through this connector is constrained to be zero ($\text{spline.tau} = 0$), meaning the component prescribes motion kinematically without imparting any dynamic load itself. It effectively acts as an ideal angular velocity source at the initial moment.

Usage

PrescribeInitialVelocity(w0)

Parameters:

Connectors

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

Variables

Behavior

\[ \begin{align} \frac{\mathrm{d} \mathtt{spline.phi}\left( t \right)}{\mathrm{d}t} &= w\left( t \right) \\ \mathtt{spline.tau}\left( t \right) &= 0 \end{align} \]

Source

# Sets a defined initial angular velocity to a rotational mechanical connector.
#
# This component is used to define and enforce a specific initial angular velocity
# (`w_0`) on a rotational mechanical system at the commencement of a
# simulation. It interfaces with the system through a `spline`, which
# acts as a rotational connector. The component ensures that at time t=0, the
# angular velocity `w` of the connector is precisely equal to the user-defined
# parameter `w_0`. The relationship \$\frac{d\text{spline.phi}}{dt} = w\$
# establishes that `w` is indeed the angular velocity of the `spline` connector.
# Importantly, the torque transmitted through this connector is constrained to be
# zero (\$\text{spline.tau} = 0\$), meaning the component prescribes motion
# kinematically without imparting any dynamic load itself. It effectively acts as
# an ideal angular velocity source at the initial moment.
component PrescribeInitialVelocity
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Desired initial angular velocity at the start of the simulation
  parameter w0::Velocity
  # Actual angular velocity of the component, initialized to w0
  variable w::Velocity
relations
  initial w = w0
  der(spline.phi) = w
  spline.tau = 0
metadata {
  "Dyad": {
    "labels": [{"label": "initial w=$(w0)", "x": 500, "y": 800, "rot": 0}],
    "icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}
  }
}
end

# Sets a defined initial angular velocity to a rotational mechanical connector.
#
# This component is used to define and enforce a specific initial angular velocity
# (`w_0`) on a rotational mechanical system at the commencement of a
# simulation. It interfaces with the system through a `spline`, which
# acts as a rotational connector. The component ensures that at time t=0, the
# angular velocity `w` of the connector is precisely equal to the user-defined
# parameter `w_0`. The relationship \$\frac{d\text{spline.phi}}{dt} = w\$
# establishes that `w` is indeed the angular velocity of the `spline` connector.
# Importantly, the torque transmitted through this connector is constrained to be
# zero (\$\text{spline.tau} = 0\$), meaning the component prescribes motion
# kinematically without imparting any dynamic load itself. It effectively acts as
# an ideal angular velocity source at the initial moment.
component PrescribeInitialVelocity
  spline = Spline() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Desired initial angular velocity at the start of the simulation
  parameter w0::Velocity
  # Actual angular velocity of the component, initialized to w0
  variable w::Velocity
relations
  initial w = w0
  der(spline.phi) = w
  spline.tau = 0
metadata {
  "Dyad": {
    "labels": [{"label": "initial w=$(w0)", "x": 500, "y": 800, "rot": 0}],
    "icons": {"default": "dyad://RotationalComponents/Pos-Speed-Acc-Move.svg"}
  }
}
end

Test Cases

No test cases defined.

Related

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